Results for ' finitely generic'

980 found
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  1.  39
    Finitely generic models of tUH, for certain model companionable theories T.Francoise Point - 1985 - Journal of Symbolic Logic 50 (3):604 - 610.
  2.  33
    Finite generics of p-compatible varieties.Teresa Bieganska - 2003 - Bulletin of the Section of Logic 32 (1/2):1-7.
    For every variety V there exists an algebra A generating V by means of direct products, subalgebras and homomorphic images, i.e. V = HSP(A). Such algebras are called generics of V. Obviously, the free algebra over V with omega generators is a generic of V . The aim of this paper is to find finite generics for some P-compatible varieties.
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  3. Generic properties of subgroups of free groups and finite presentations.Frédérique Bassino, Cyril Nicaud & Pascal Weil - 2016 - In Delaram Kahrobaei, Bren Cavallo & David Garber, Algebra and computer science. Providence, Rhode Island: American Mathematical Society.
     
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  4.  52
    Finitely approximable groups and actions Part II: Generic representations.Christian Rosendal - 2011 - Journal of Symbolic Logic 76 (4):1307-1321.
    Given a finitely generated group Γ, we study the space Isom(Γ, ℚ������) of all actions of Γ by isometries of the rational Urysohn metric space ℚ������, where Isom(Γ, ℚ������) is equipped with the topology it inherits seen as a closed subset of Isom(ℚ������) Γ . When Γ is the free group ������ n on n generators this space is just Isom(ℚ������) n , but is in general significantly more complicated. We prove that when Γ is finitely generated Abelian (...)
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  5.  19
    More on Generic Dimension Groups.Philip Scowcroft - 2015 - Notre Dame Journal of Formal Logic 56 (4):511-553.
    While finitely generic dimension groups are known to admit no proper self-embeddings, these groups also have no automorphisms other than scalar multiplications, and every countable infinitely generic dimension group admits proper self-embeddings and has automorphisms other than scalar multiplications. The finite-forcing companion of the theory of dimension groups is recursively isomorphic to first-order arithmetic, the infinite-forcing companion of the theory of dimension groups is recursively isomorphic to second-order arithmetic, and the first-order theory of existentially closed dimension groups (...)
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  6.  43
    Superrosy dependent groups having finitely satisfiable generics.Clifton Ealy, Krzysztof Krupiński & Anand Pillay - 2008 - Annals of Pure and Applied Logic 151 (1):1-21.
    We develop a basic theory of rosy groups and we study groups of small Uþ-rank satisfying NIP and having finitely satisfiable generics: Uþ-rank 1 implies that the group is abelian-by-finite, Uþ-rank 2 implies that the group is solvable-by-finite, Uþ-rank 2, and not being nilpotent-by-finite implies the existence of an interpretable algebraically closed field.
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  7.  41
    Normalizable linear orders and generic computations in finite models.Alexei P. Stolboushkin & Michael A. Taitslin - 1999 - Archive for Mathematical Logic 38 (4-5):257-271.
    Numerous results about capturing complexity classes of queries by means of logical languages work for ordered structures only, and deal with non-generic, or order-dependent, queries. Recent attempts to improve the situation by characterizing wide classes of finite models where linear order is definable by certain simple means have not been very promising, as certain commonly believed conjectures were recently refuted (Dawar's Conjecture). We take on another approach that has to do with normalization of a given order (rather than with (...)
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  8.  70
    Generic Expansions of Countable Models.Silvia Barbina & Domenico Zambella - 2012 - Notre Dame Journal of Formal Logic 53 (4):511-523.
    We compare two different notions of generic expansions of countable saturated structures. One kind of genericity is related to existential closure, and another is defined via topological properties and Baire category theory. The second type of genericity was first formulated by Truss for automorphisms. We work with a later generalization, due to Ivanov, to finite tuples of predicates and functions. Let $N$ be a countable saturated model of some complete theory $T$ , and let $(N,\sigma)$ denote an expansion of (...)
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  9.  48
    On generic structures with a strong amalgamation property.Koichiro Ikeda, Hirotaka Kikyo & Akito Tsuboi - 2009 - Journal of Symbolic Logic 74 (3):721-733.
    Let L be a finite relational language and α=(αR:R ∈ L) a tuple with 0 < αR ≤1 for each R ∈ L. Consider a dimension function $ \delta _\alpha (A) = \left| A \right| - \sum\limits_{R \in L} {\alpha {\mathop{\rm Re}\nolimits} R(A)} $ where each eR(A) is the number of realizations of R in A. Let $K_\alpha $ be the class of finite structures A such that $\delta _\alpha (X) \ge 0$ 0 for any substructure X of A. We (...)
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  10.  39
    Simple generic structures.Massoud Pourmahdian - 2003 - Annals of Pure and Applied Logic 121 (2-3):227-260.
    A study of smooth classes whose generic structures have simple theory is carried out in a spirit similar to Hrushovski 147; Simplicity and the Lascar group, preprint, 1997) and Baldwin–Shi 1). We attach to a smooth class K0, of finite -structures a canonical inductive theory TNat, in an extension-by-definition of the language . Here TNat and the class of existentially closed models of =T+,EX, play an important role in description of the theory of the K0,-generic. We show that (...)
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  11.  23
    A Generic Figures Reconstruction of Peirce’s Existential Graphs (Alpha).Fernando Tohme, Gianluca Caterina & Rocco Gangle - 2020 - Erkenntnis 87 (2):623-656.
    We present a category-theoretical analysis, based on the concept of generic figures, of a diagrammatic system for propositional logic (Peirce’s Existential Graphs α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}). The straightforward construction of a presheaf category EGα∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {E}}}{{\mathcal {G}}}_{\alpha ^{*}}$$\end{document} of cuts-only Existential Graphs (equivalent to the well-studied category of finite forests) provides a basis for the further construction of the category EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} (...)
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  12.  31
    Remarks on generic stability in independent theories.Gabriel Conant & Kyle Gannon - 2020 - Annals of Pure and Applied Logic 171 (2):102736.
    In NIP theories, generically stable Keisler measures can be characterized in several ways. We analyze these various forms of “generic stability” in arbitrary theories. Among other things, we show that the standard definition of generic stability for types coincides with the notion of a frequency interpretation measure. We also give combinatorial examples of types in NSOP theories that are finitely approximated but not generically stable, as well as ϕ-types in simple theories that are definable and finitely (...)
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  13.  26
    On ω-categorical, generically stable groups.Jan Dobrowolski & Krzysztof Krupiński - 2012 - Journal of Symbolic Logic 77 (3):1047-1056.
    We prove that each ω-categorical, generically stable group is solvable-by-finite.
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  14.  15
    Generic automorphisms with prescribed fixed fields.Bijan Afshordel - 2014 - Journal of Symbolic Logic 79 (4):985-1000.
    This article addresses the question which structures occur as fixed structures of stable structures with a generic automorphism. In particular we give a Galois theoretic characterization. Furthermore, we prove that any pseudofinite field is the fixed field of some model ofACFA, any one-free pseudo-differentially closed field of characteristic zero is the fixed field of some model ofDCFA, and that any one-free PAC field of finite degree of imperfection is the fixed field of some model ofSCFA.
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  15.  11
    Metrically Universal Generic Structures in Free Amalgamation Classes.Anthony Bonato - 2001 - Mathematical Logic Quarterly 47 (2):147-160.
    We prove that each ∀1 free amalgamation class K over a finite relational language L admits a countable generic structure M isometrically embedding all countable structuresin K relative to a fixed metric. We expand L by infinitely many binary predicates expressingdistance, and prove that the resulting expansion of K has a model companion axiomatizedby the first-order theory of M. The model companion is non-finitely axiomatizable, evenover a strong form of the axiom scheme of infinity.
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  16.  55
    On ω-categorical, generically stable groups and rings.Jan Dobrowolski & Krzysztof Krupiński - 2013 - Annals of Pure and Applied Logic 164 (7-8):802-812.
    We prove that every ω-categorical, generically stable group is nilpotent-by-finite and that every ω-categorical, generically stable ring is nilpotent-by-finite.
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  17.  46
    Stable generic structures.John T. Baldwin & Niandong Shi - 1996 - Annals of Pure and Applied Logic 79 (1):1-35.
    Hrushovski originated the study of “flat” stable structures in constructing a new strongly minimal set and a stable 0-categorical pseudoplane. We exhibit a set of axioms which for collections of finite structure with dimension function δ give rise to stable generic models. In addition to the Hrushovski examples, this formalization includes Baldwin's almost strongly minimal non-Desarguesian projective plane and several others. We develop the new case where finite sets may have infinite closures with respect to the dimension function δ. (...)
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  18.  28
    Ab initio generic structures which are superstable but not ω-stable.Koichiro Ikeda - 2012 - Archive for Mathematical Logic 51 (1):203-211.
    Let L be a countable relational language. Baldwin asked whether there is an ab initio generic L-structure which is superstable but not ω-stable. We give a positive answer to his question, and prove that there is no ab initio generic L-structure which is superstable but not ω-stable, if L is finite and the generic is saturated.
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  19.  64
    Generic expansions of ω-categorical structures and semantics of generalized quantifiers.A. A. Ivanov - 1999 - Journal of Symbolic Logic 64 (2):775-789.
    LetMbe a countably infinite ω-categorical structure. Consider Aut(M) as a complete metric space by definingd(g, h) = Ω{2−n:g(xn) ≠h(xn) org−1(xn) ≠h−1(xn)} where {xn:n∈ ω} is an enumeration ofMAn automorphism α ∈ Aut(M) is generic if its conjugacy class is comeagre. J. Truss has shown in [11] that if the set P of all finite partial isomorphisms contains a co-final subset P1closed under conjugacy and having the amalgamation property and the joint embedding property then there is a generic automorphism. (...)
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  20.  47
    CM-triviality and generic structures.Ikuo Yoneda - 2003 - Archive for Mathematical Logic 42 (5):423-433.
    We show that any relational generic structure whose theory has finite closure and amalgamation over closed sets is stable CM-trivial with weak elimination of imaginaries.
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  21. Jamesian Finite Theism and the Problems of Suffering.Walter Scott Stepanenko - 2018 - European Journal for Philosophy of Religion 10 (4):1-25.
    William James advocated a form of finite theism, motivated by epistemological and moral concerns with scholastic theism and pantheism. In this article, I elaborate James’s case for finite theism and his strategy for dealing with these concerns, which I dub the problems of suffering. I contend that James is at the very least implicitly aware that the problem of suffering is not so much one generic problem but a family of related problems. I argue that one of James’s great (...)
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  22.  90
    A Note on Generically Stable Measures and fsg Groups.Ehud Hrushovski, Anand Pillay & Pierre Simon - 2012 - Notre Dame Journal of Formal Logic 53 (4):599-605.
    We prove (Proposition 2.1) that if $\mu$ is a generically stable measure in an NIP (no independence property) theory, and $\mu(\phi(x,b))=0$ for all $b$ , then for some $n$ , $\mu^{(n)}(\exists y(\phi(x_{1},y)\wedge \cdots \wedge\phi(x_{n},y)))=0$ . As a consequence we show (Proposition 3.2) that if $G$ is a definable group with fsg (finitely satisfiable generics) in an NIP theory, and $X$ is a definable subset of $G$ , then $X$ is generic if and only if every translate of $X$ (...)
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  23.  48
    Generic Complexity of Undecidable Problems.Alexei G. Myasnikov & Alexander N. Rybalov - 2008 - Journal of Symbolic Logic 73 (2):656 - 673.
    In this paper we study generic complexity of undecidable problems. It turns out that some classical undecidable problems are, in fact, strongly undecidable, i.e., they are undecidable on every strongly generic subset of inputs. For instance, the classical Halting Problem is strongly undecidable. Moreover, we prove and analog of the Rice theorem for strongly undecidable problems, which provides plenty of examples of strongly undecidable problems. Then we show that there are natural super-undecidable problems. i.e., problem which are undecidable (...)
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  24.  39
    Extended order-generic queries.Oleg V. Belegradek, Alexei P. Stolboushkin & Michael A. Taitslin - 1999 - Annals of Pure and Applied Logic 97 (1-3):85-125.
    We consider relational databases organized over an ordered domain with some additional relations — a typical example is the ordered domain of rational numbers together with the operation of addition. In the focus of our study are the first-order queries that are invariant under order-preserving “permutations” — such queries are called order-generic. It has recently been discovered that for some domains order-generic FO queries fail to express more than pure order queries. For example, every order-generic FO query (...)
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  25.  70
    Generic substitutions.Giovanni Panti - 2005 - Journal of Symbolic Logic 70 (1):61-83.
    Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic properties of the action. In classical logic there is a strong dichotomy: while over finitely many propositional variables everything is trivial, the study of the continuous transformations of the Cantor space is the subject of an extensive literature, and is far (...)
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  26.  23
    On pseudolinearity and generic pairs.Evgueni Vassiliev - 2010 - Mathematical Logic Quarterly 56 (1):35-41.
    We continue the study of the connection between the “geometric” properties of SU -rank 1 structures and the properties of “generic” pairs of such structures, started in [8]. In particular, we show that the SU-rank of the theory of generic pairs of models of an SU -rank 1 theory T can only take values 1 , 2 or ω, generalizing the corresponding results for a strongly minimal T in [3]. We also use pairs to derive the implication from (...)
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  27.  18
    Existentially Closed Closure Algebras.Philip Scowcroft - 2020 - Notre Dame Journal of Formal Logic 61 (4):623-661.
    The study of existentially closed closure algebras begins with Lipparini’s 1982 paper. After presenting new nonelementary axioms for algebraically closed and existentially closed closure algebras and showing that these nonelementary classes are different, this paper shows that the classes of finitely generic and infinitely generic closure algebras are closed under finite products and bounded Boolean powers, extends part of Hausdorff’s theory of reducible sets to existentially closed closure algebras, and shows that finitely generic and infinitely (...)
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  28.  57
    Reals n-Generic Relative to Some Perfect Tree.Bernard A. Anderson - 2008 - Journal of Symbolic Logic 73 (2):401 - 411.
    We say that a real X is n-generic relative to a perfect tree T if X is a path through T and for all $\Sigma _{n}^{0}(T)$ sets S, there exists a number k such that either X|k ∈ S or for all σ ∈ T extending X|k we have σ ∉ S. A real X is n-generic relative to some perfect tree if there exists such a T. We first show that for every number n all but countably (...)
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  29.  16
    On Groups with Definable F-Generics Definable in P-Adically Closed Fields.Anand Pillay & Y. A. O. Ningyuan - 2023 - Journal of Symbolic Logic 88 (4):1334-1353.
    The aim of this paper is to develop the theory of groups definable in the p-adic field ${{\mathbb {Q}}_p}$, with “definable f-generics” in the sense of an ambient saturated elementary extension of ${{\mathbb {Q}}_p}$. We call such groups definable f-generic groups.So, by a “definable f-generic” or $dfg$ group we mean a definable group in a saturated model with a global f-generic type which is definable over a small model. In the present context the group is definable over (...)
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  30.  18
    Bowtie‐free graphs and generic automorphisms.Daoud Siniora - 2023 - Mathematical Logic Quarterly 69 (2):221-230.
    We show that the countable universal ω‐categorical bowtie‐free graph admits generic automorphisms. Moreover, we show that this graph is not finitely homogenisable.
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  31.  37
    Hyperbolic Towers and Independent Generic Sets in the Theory of Free Groups.Larsen Louder, Chloé Perin & Rizos Sklinos - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):521-539.
    We use hyperbolic towers to answer some model-theoretic questions around the generic type in the theory of free groups. We show that all the finitely generated models of this theory realize the generic type $p_{0}$ but that there is a finitely generated model which omits $p^{}_{0}$. We exhibit a finitely generated model in which there are two maximal independent sets of realizations of the generic type which have different cardinalities. We also show that a (...)
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  32.  56
    On the generic type of the free group.Rizos Sklinos - 2011 - Journal of Symbolic Logic 76 (1):227 - 234.
    We answer a question raised in [9], that is whether the infinite weight of the generic type of the free group is witnessed in F ω . We also prove that the set of primitive elements in finite rank free groups is not uniformly definable. As a corollary, we observe that the generic type over the empty set is not isolated. Finally, we show that uncountable free groups are not N₁-homogeneous.
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  33.  98
    Almost weakly 2-generic sets.Stephen A. Fenner - 1994 - Journal of Symbolic Logic 59 (3):868-887.
    There is a family of questions in relativized complexity theory--weak analogs of the Friedberg Jump-Inversion Theorem--that are resolved by 1-generic sets but which cannot be resolved by essentially any weaker notion of genericity. This paper defines aw2-generic sets. i.e., sets which meet every dense set of strings that is r.e. in some incomplete r.e. set. Aw2-generic sets are very close to 1-generic sets in strength, but are too weak to resolve these questions. In particular, it is (...)
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  34.  21
    Automorphism invariant measures and weakly generic automorphisms.Gábor Sági - 2022 - Mathematical Logic Quarterly 68 (4):458-478.
    Let be a countable ℵ0‐homogeneous structure. The primary motivation of this work is to study different amenability properties of (subgroups of) the automorphism group of ; the secondary motivation is to study the existence of weakly generic automorphisms of. Among others, we present sufficient conditions implying the existence of automorphism invariant probability measures on certain subsets of A and of ; we also present sufficient conditions implying that the theory of is amenable. More concretely, we show that if the (...)
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  35.  49
    Complexity of the -query Tautologies in the Presence of a Generic Oracle.Toshio Suzuki - 2000 - Notre Dame Journal of Formal Logic 41 (2):142-151.
    Extending techniques of Dowd and those of Poizat, we study computational complexity of in the case when is a generic oracle, where is a positive integer, and denotes the collection of all -query tautologies with respect to an oracle . We introduce the notion of ceiling-generic oracles, as a generalization of Dowd's notion of -generic oracles to arbitrary finitely testable arithmetical predicates. We study how existence of ceiling-generic oracles affects behavior of a generic oracle, (...)
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  36.  28
    A note on stability spectrum of generic structures.Yuki Anbo & Koichiro Ikeda - 2010 - Mathematical Logic Quarterly 56 (3):257-261.
    We show that if a class K of finite relational structures is closed under quasi-substructures, then there is no saturated K-generic structure that is superstable but not ω -stable.
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  37.  46
    Semisimple torsion in groups of finite Morley rank.Jeffrey Burdges & Gregory Cherlin - 2009 - Journal of Mathematical Logic 9 (2):183-200.
    We prove several results about groups of finite Morley rank without unipotent p-torsion: p-torsion always occurs inside tori, Sylow p-subgroups are conjugate, and p is not the minimal prime divisor of our approximation to the "Weyl group". These results are quickly finding extensive applications within the classification project.
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  38.  20
    The profinite topology of free groups and weakly generic tuples of automorphisms.Gábor Sági - 2021 - Mathematical Logic Quarterly 67 (4):432-444.
    Let be a countable first order structure and endow the universe of with the discrete topology. Then the automorphism group of becomes a topological group. A tuple of automorphisms is defined to be weakly generic iff its diagonal conjugacy class (in the algebraic sense) is dense (in the topological sense) and the ‐orbit of each is finite. Existence of tuples of weakly generic automorphisms are interesting from the point of view of model theory as well as from the (...)
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  39.  35
    Extensions of ordered theories by generic predicates.Alfred Dolich, Chris Miller & Charles Steinhorn - 2013 - Journal of Symbolic Logic 78 (2):369-387.
    Given a theoryTextending that of dense linear orders without endpoints, in a language ℒ ⊇ {<}, we are interested in extensionsT′ ofTin languages extending ℒ by unary relation symbols that are each interpreted in models ofT′ as sets that are both dense and codense in the underlying sets of the models.There is a canonically “wild” example, namelyT= Th andT′ = Th. Recall thatTis o-minimal, and so every open set definable in any model ofThas only finitely many definably connected components. (...)
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  40.  40
    The definable multiplicity property and generic automorphisms.Hirotaka Kikyo & Anand Pillay - 2000 - Annals of Pure and Applied Logic 106 (1-3):263-273.
    Let T be a strongly minimal theory with quantifier elimination. We show that the class of existentially closed models of T{“σ is an automorphism”} is an elementary class if and only if T has the definable multiplicity property, as long as T is a finite cover of a strongly minimal theory which does have the definable multiplicity property. We obtain cleaner results working with several automorphisms, and prove: the class of existentially closed models of T{“σi is an automorphism”: i=1,2} is (...)
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  41.  22
    Abelian groups definable in P-adically closed fields.Will Johnson & Y. A. O. Ningyuan - forthcoming - Journal of Symbolic Logic:1-22.
    Recall that a group G has finitely satisfiable generics (fsg) or definable f-generics (dfg) if there is a global type p on G and a small model $M_0$ such that every left translate of p is finitely satisfiable in $M_0$ or definable over $M_0$, respectively. We show that any abelian group definable in a p-adically closed field is an extension of a definably compact fsg definable group by a dfg definable group. We discuss an approach which might prove (...)
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  42.  28
    Weight and Measure in NIP Theories.Anand Pillay - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):567-578.
    We initiate an account of Shelah’s notion of “strong dependence” in terms of generically stable measures, proving a measure analogue of the fact that a stable theory $T$ is “strongly dependent” if and only if all types have almost finite weight.
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  43.  40
    Ages of Expansions of ω-Categorical Structures.A. Ivanov & K. Majcher - 2007 - Notre Dame Journal of Formal Logic 48 (3):371-380.
    The age of a structure M is the set of all isomorphism types of finite substructures of M. We study ages of generic expansions of ω-stable ω-categorical structures.
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  44.  14
    Symétries Et Transvexions, Principalement Dans Les Groupes de Rang de Morley Fini Sans Involutions.Bruno Poizat - 2021 - Journal of Symbolic Logic 86 (3):965-990.
    The role played by the symmetric structure of a group of finite Morley rank without involutions in the proof by contradiction of Frécon 2018 was put in evidence in Poizat 2018; indeed, this proof consists in the construction of a symmetric space of dimension two (“a plane”), and then in showing that such a plane cannot exist.To a definable symmetric subset of such a group are associated symmetries and transvections, that we undertake here to study in the abstract, without mentioning (...)
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  45.  34
    Augustine’s Confessions and the Transcendental Ground of Consciousness, or How Literary Narrative Becomes Prophetic Revelation.William Franke - 2014 - Philosophy and Literature 38 (1):204-222.
    The generic paradigms for Augustine’s discourse include not only autobiography but also theology, philosophy, exegesis, and “confession.” However, most importantly of all, Augustine’s discourse is cast into the form of a dialogue with God. His life story, unfolding in a succession of anecdotes, forms a horizontal axis that is traversed by and wholly subsumed under a vertical axis, along which he converses directly with God. The point of view evoked through this dialogue is not a temporally finite point of (...)
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  46.  25
    Automorphisms of Homogeneous Structures.A. Ivanov - 2005 - Notre Dame Journal of Formal Logic 46 (4):419-424.
    We give an example of a simple ω-categorical theory such that for any finite set of parameters the corresponding constant expansion does not satisfy the PAPA. We describe a wide class of homogeneous structures with generic automorphisms and show that some natural reducts of our example belong to this class.
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  47. Validity as Truth-Conduciveness.Arvid Båve - 2024 - In Adam C. Podlaskowski & Drew Johnson, Truth 20/20: How a Global Pandemic Shaped Truth Research. Synthese Library.
    Thomas Hofweber takes the semantic paradoxes to motivate a radical reconceptualization of logical validity, rejecting the idea that an inference rule is valid just in case every instance thereof is necessarily truth-preserving. Rather than this “strict validity”, we should identify validity with “generic validity”, where a rule is generically valid just in case its instances are truth preserving, and where this last sentence is a generic, like “Bears are dangerous”. While sympathetic to Hofweber’s view that strict validity should (...)
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    Normal Extensions of G.3.Ming Xu - 2002 - Theoria 68 (2):170-176.
    In this paper we use “generic submodels” to prove that each normal extension of G.3 (K4.3W) has the finite model property, by which we establish that each proper normal extension of G.3 is G.3Altn for some n≥0.
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    Local Keisler measures and nip formulas.Kyle Gannon - 2019 - Journal of Symbolic Logic 84 (3):1279-1292.
    We study generically stable measures in the local, NIP context. We show that in this setting, a measure is generically stable if and only if it admits a natural finite approximation.
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    Generix Never Gives Up.Eric Jaligot - 2006 - Journal of Symbolic Logic 71 (2):599 - 610.
    We prove conjugacy and generic disjointness of generous Carter subgroups in groups of finite Morley rank. We elaborate on groups with a generous Carter subgroup and on a minimal counterexample to the Genericity Conjecture.
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