In this paper, we show that equation image is a equation image-conservative extension of BΣ1 + exp, thus it does not imply IΣ1.

We investigate the reverse-mathematical status of several theorems to the effect that the natural number system is second-order categorical. One of our results is as follows. Define a system to be a triple A,i,f such that A is a set and i∈A and f:A→A. A subset X⊆A is said to be inductive if i∈X and ∀a ∈X). The system A,i,f is said to be inductive if the only inductive subset of A is A itself. Define a Peano system to be (...) an inductive system such that f is one-to-one and i∉the range of f. The standard example of a Peano system is N,0,S where N={0,1,2,…,n,…}=the set of natural numbers and S:N→N is given by S=n+1 for all n∈N. Consider the statement that all Peano systems are isomorphic to N,0,S. We prove that this statement is logically equivalent to WKL0 over RCA0⁎ source. From this and similar equivalences we draw some foundational/philosophical consequences. (shrink)

We study the parameterized complexity of the problem to decide whether a given natural number n satisfies a given $\Delta _0$ -formula $\varphi (x)$ ; the parameter is the size of $\varphi $. This parameterization focusses attention on instances where n is large compared to the size of $\varphi $. We show unconditionally that this problem does not belong to the parameterized analogue of $\mathsf {AC}^0$. From this we derive that certain natural upper bounds on the complexity of our parameterized (...) problem imply certain separations of classical complexity classes. This connection is obtained via an analysis of a parameterized halting problem. Some of these upper bounds follow assuming that $I\Delta _0$ proves the MRDP theorem in a certain weak sense. (shrink)

We study the first-order consequences of Ramsey’s Theorem fork-colourings ofn-tuples, for fixed$n, k \ge 2$, over the relatively weak second-order arithmetic theory$\mathrm {RCA}^*_0$. Using the Chong–Mourad coding lemma, we show that in a model of$\mathrm {RCA}^*_0$that does not satisfy$\Sigma ^0_1$induction,$\mathrm {RT}^n_k$is equivalent to its relativization to any proper$\Sigma ^0_1$-definable cut, so its truth value remains unchanged in all extensions of the model with the same first-order universe.We give a complete axiomatization of the first-order consequences of$\mathrm {RCA}^*_0 + \mathrm {RT}^n_k$for$n \ge (...) 3$. We show that they form a non-finitely axiomatizable subtheory of$\mathrm {PA}$whose$\Pi _3$fragment coincides with$\mathrm {B} \Sigma _1 + \exp $and whose$\Pi _{\ell +3}$fragment for$\ell \ge 1$lies between$\mathrm {I} \Sigma _\ell \Rightarrow \mathrm {B} \Sigma _{\ell +1}$and$\mathrm {B} \Sigma _{\ell +1}$. We also give a complete axiomatization of the first-order consequences of$\mathrm {RCA}^*_0 + \mathrm {RT}^2_k + \neg \mathrm {I} \Sigma _1$. In general, we show that the first-order consequences of$\mathrm {RCA}^*_0 + \mathrm {RT}^2_k$form a subtheory of$\mathrm {I} \Sigma _2$whose$\Pi _3$fragment coincides with$\mathrm {B} \Sigma _1 + \exp $and whose$\Pi _4$fragment is strictly weaker than$\mathrm {B} \Sigma _2$but not contained in$\mathrm {I} \Sigma _1$.Additionally, we consider a principle$\Delta ^0_2$-$\mathrm {RT}^2_2$which is defined like$\mathrm {RT}^2_2$but with both the$2$-colourings and the solutions allowed to be$\Delta ^0_2$-sets rather than just sets. We show that the behaviour of$\Delta ^0_2$-$\mathrm {RT}^2_2$over$\mathrm {RCA}_0 + \mathrm {B}\Sigma ^0_2$is in many ways analogous to that of$\mathrm {RT}^2_2$over$\mathrm {RCA}^*_0$, and that$\mathrm {RCA}_0 + \mathrm {B} \Sigma ^0_2 + \Delta ^0_2$-$\mathrm {RT}^2_2$is$\Pi _4$- but not$\Pi _5$-conservative over$\mathrm {B} \Sigma _2$. However, the statement we use to witness failure of$\Pi _5$-conservativity is not provable in$\mathrm {RCA}_0 +\mathrm {RT}^2_2$. (shrink)

The paper interprets Nietzsche’s description of authentic human person.Based on the works of Nietzsche, commentaries and philosophical interpretationsof various authors, authentic human person evolves into a superman by usingthe principles of discipline and mastery of oneself. His authenticity, however,requires persistence, courage and strength to endure many forms of sufferingsand to overcome alienation brought about by his environment. Otherwise,man would become slave of his desires or alien to his own powers, talents andcapacities. Thus, Nietzsche’s thought of superman is an invitation to (...) overcomeoneself, the self that is influenced by the non-self or factors outside one self. Itis only possible by using the will to power. The will to power of man overcomesthe influences of the world’s modernization and industrialization that alienateshim to his true self, and this true self is best expressed by his will to power. Onthis note, the author suggests that the readers must use their potentials to face up to challenges of this new era. Keywords: Philosophy, language and literature, emergence, authentic human person,philosophy of the superman, authenticity, alienation, morality, descriptivedesign, Philippines. (shrink)

No crucial experiment demonstrates that four hue categories are needed to describe color appearance. Instead, converging lines of evidence suggest that the terms red, yellow, green, and blue are sufficient and precise enough for deriving color discrimination functions and for a useful model constraining relations between color appearance and neuronal responses. Such a model need not be based on linguistic universals. Until something better is available, this holds.

The article considers the process of identity constructing in modern culture. As a result of the case analysis, the author conceptualizes the modern identity construction strategy as an individualization of identity. The worldview foundations of this strategy are revealed. It is proposed to distinguish two paradigms of identity on the basis of the function of social representation: I-as-image and I-as-symbol. The author connects the tendency of individualization and delegitimation of social institutions in modern culture with the process of transition from (...) a symbolically oriented type of consciousness to a type of consciousness focused on figurative perception. (shrink)

UPDATE WITH NOMINAL CENTERING (UCδ) D1.0 (UCδ types) The set of UCδ types Θ is the smallest set such that: i. t, δ, s ∈ Θ ii. (ab) ∈ Θ, if a, b ∈ Θ D1.1 (UCδ basic terms). For each a ∈ Θ, a set of a-constants Cona and a-variables Vara, incl.: Conδ = {a, b, c} Var(sδ) = {x, y, z}.

In this paper, we introduce the systems ns-ACA₀ and ns-WKL₀ of non-standard second-order arithmetic in which we can formalize non-standard arguments in ACA₀ and WKL₀, respectively. Then, we give direct transformations from non-standard proofs in ns-ACA₀ or ns-WKL₀ into proofs in ACA₀ or WKL₀.

This research is motivated by the program of Reverse Mathematics. We investigate basic part of complex analysis within some weak subsystems of second order arithmetic, in order to determine what kind of set existence axioms are needed to prove theorems of basic analysis. We are especially concerned with Cauchy’s integral theorem. We show that a weak version of Cauchy’s integral theorem is proved in RCAo. Using this, we can prove that holomorphic functions are analytic in RCAo. On the other hand, (...) we show that a full version of Cauchy’s integral theorem cannot be proved in RCAo but is equivalent to weak König’s lemma over RCAo. (shrink)

Disbelief, lies, and manipulations have been objects of scholarly consideration from widely different perspectives: historical, sociological, philosophical, ethical, logical, and pragmatic. In this paper, these notions are re-examined in the framework of a Transactional Discourse Model which operates in terms of the location and relocation of various knowledge items within two sets of knowledge, A and B, representing two interlocators A and B, and two of their subsets Ca and Cb, which constitute the sets of the matters of A's and (...) B's current concern. This approach reveals certain formal features shared by lies, disbelief, and manipulations that indicate that these three types of discourse behavior constitute a deviation from successful interpersonal communication as defined in the proposed model. The model, moreover, enables us to explicitly capture both the similarities and the differences of lies and manipulations with other pragmatic phenomena, such as jokes, impersonating, role-acting, memory failure, politeness expressions, and tact; the comparison suggests that certain modifications of Gricean conversational maxims may be in order. (shrink)

We show that many principles of first-order arithmetic, previously only known to lie strictly between [Formula: see text]-induction and [Formula: see text]-induction, are equivalent to the well-foundedness of [Formula: see text]. Among these principles are the iteration of partial functions of Hájek and Paris, the bounded monotone enumerations principle by Chong, Slaman, and Yang, the relativized Paris–Harrington principle for pairs, and the totality of the relativized Ackermann–Péter function. With this we show that the well-foundedness of [Formula: see text] is a (...) far more widespread than usually suspected. Further, we investigate the [Formula: see text]-iterated version of the bounded monotone iterations principle, and show that it is equivalent to the well-foundedness of the -height [Formula: see text]-tower [Formula: see text]. (shrink)

In this paper, we show within ${\mathsf{RCA}_0}$ that both the Jordan curve theorem and the Schönflies theorem are equivalent to weak König’s lemma. Within ${\mathsf {WKL}_0}$ , we prove the Jordan curve theorem using an argument of non-standard analysis based on the fact that every countable non-standard model of ${\mathsf {WKL}_0}$ has a proper initial part that is isomorphic to itself (Tanaka in Math Logic Q 43:396–400, 1997).

In this paper, we introduce a system of nonstandard second-order arithmetic $\mathsf{ns}$-$\mathsf{WWKL_0}$ which consists of $\mathsf{ns}$-$\mathsf{BASIC}$ plus Loeb measure property. Then we show that $\mathsf{ns}$-$\mathsf{WWKL_0}$ is a conservative extension of $\mathsf{WWKL_0}$ and we do Reverse Mathematics for this system.

Background There are several psychosocial and ethical issues surrounding the decision to be a living kidney donor. The present study aimed to determine the perceptions of psychosocial and ethical issues that living kidney donors may have, and analyze their psychological characteristics.Methods Face-to-face semi-structured interviews were conducted with 15 donors. Thematic analysis was then performed to categorize the thematic elements of the transcripts. All procedures were approved by the relevant review board.Results Four main categories were identified: Awareness of family dynamics, barriers (...) to a proper understanding, contrasting psychological effects of recipient presence in clinical practice, insufficient information explained in informed consent.Conclusion Donors felt that they took on the “role as a care giver” for the recipient and were less aware of themselves as patients. This is a new concept that has not been shown in previous studies. Donors exist within the recipient and family, and the range of their autonomy may go beyond the traditional concept of autonomy and be rooted in relational autonomy. This study suggested that medical treatment in the presence of the recipient promotes the relational autonomy of the donor. (shrink)

The program of Reverse Mathematics (Simpson 2009) has provided us with the insight that most theorems of ordinary mathematics are either equivalent to one of a select few logical principles, or provable in a weak base theory. In this paper, we study the properties of the Dirac delta function (Dirac 1927; Schwartz 1951) in two settings of Reverse Mathematics. In particular, we consider the Dirac Delta Theorem, which formalizes the well-known property \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} (...) \begin{document}$${\int_\mathbb{R}f(x)\delta(x)\,dx=f(0)}$$\end{document} of the Dirac delta function. We show that the Dirac Delta Theorem is equivalent to weak König’s Lemma (see Yu and Simpson in Arch Math Log 30(3):171–180, 1990) in classical Reverse Mathematics. This further validates the status of WWKL0 as one of the ‘Big’ systems of Reverse Mathematics. In the context of ERNA’s Reverse Mathematics (Sanders in J Symb Log 76(2):637–664, 2011), we show that the Dirac Delta Theorem is equivalent to the Universal Transfer Principle. Since the Universal Transfer Principle corresponds to WKL, it seems that, in ERNA’s Reverse Mathematics, the principles corresponding to WKL and WWKL coincide. Hence, ERNA’s Reverse Mathematics is actually coarser than classical Reverse Mathematics, although the base theory has lower first-order strength. (shrink)