Stationarily ordered types and the number of countable models

Annals of Pure and Applied Logic 171 (3):102765 (2020)
  Copy   BIBTEX

Abstract

We introduce the notions of stationarily ordered types and theories; the latter generalizes weak o-minimality and the former is a relaxed version of weak o-minimality localized at the locus of a single type. We show that forking, as a binary relation on elements realizing stationarily ordered types, is an equivalence relation and that each stationarily ordered type in a model determines some order-type as an invariant of the model. We study weak and forking non-orthogonality of stationarily ordered types, show that they are equivalence relations and prove that invariants of non-orthogonal types are closely related. The techniques developed are applied to prove that in the case of a binary, stationarily ordered theory with fewer than countable models, the isomorphism type of a countable model is determined by a certain sequence of invariants of the model. In particular, we confirm Vaught's conjecture for binary, stationarily ordered theories.

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 103,449

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Asymmetric RK-minimal types.Predrag Tanović - 2010 - Archive for Mathematical Logic 49 (3):367-377.
Vaught’s Conjecture for Theories of Discretely Ordered Structures.Predrag Tanović - 2024 - Notre Dame Journal of Formal Logic 65 (3):247-257.
Non-isolated types in stable theories.Predrag Tanović - 2007 - Annals of Pure and Applied Logic 145 (1):1-15.
The Borel Complexity of Isomorphism for Theories with Many Types.David Marker - 2007 - Notre Dame Journal of Formal Logic 48 (1):93-97.
Simple types in discretely ordered structures.Dejan Ilić - 2014 - Archive for Mathematical Logic 53 (7-8):929-947.
Definable types in the theory of closed ordered differential fields.Quentin Brouette - 2017 - Archive for Mathematical Logic 56 (1-2):119-129.
Types directed by constants.Predrag Tanović - 2010 - Annals of Pure and Applied Logic 161 (7):944-955.

Analytics

Added to PP
2019-11-29

Downloads
30 (#787,710)

6 months
4 (#864,415)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Vaught’s Conjecture for Theories of Discretely Ordered Structures.Predrag Tanović - 2024 - Notre Dame Journal of Formal Logic 65 (3):247-257.

Add more citations

References found in this work

On dp-minimal ordered structures.Pierre Simon - 2011 - Journal of Symbolic Logic 76 (2):448 - 460.
End extensions and numbers of countable models.Saharon Shelah - 1978 - Journal of Symbolic Logic 43 (3):550-562.
Witnessing Dp-Rank.Itay Kaplan & Pierre Simon - 2014 - Notre Dame Journal of Formal Logic 55 (3):419-429.
Vaught's conjecture for o-minimal theories.Laura L. Mayer - 1988 - Journal of Symbolic Logic 53 (1):146-159.

View all 11 references / Add more references