Syntactical truth predicates for second order arithmetic

Journal of Symbolic Logic 66 (1):225-256 (2001)
  Copy   BIBTEX

Abstract

We introduce a notion ofsyntactical truth predicate(s.t.p.) for the second order arithmeticPA2. An s.t.p. is a setTof closed formulas such that:(i)T(t=u) if and only if the closed first order termstanduare convertible, i.e., have the same value in the standard interpretation(ii)T(A→B) if and only if (T(A) ⇒T(B))(iii)T(∀xA) if and only if (T(A[x←t]) for any closed first order termt)(iv)T(∀X A) if and only if (T(A[X← ∆]) for any closed set definition ∆ = {x∣D(x)}).S.t.p.'s can be seen as a counterpart to Tarski's notion of (model-theoretical)validityand have main model properties. In particular, their existence is equivalent to the existence of anω-model ofPA2, this fact being provable inPA2with arithmetical comprehension only.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,593

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

Second-Order Arithmetic Sans Sets.L. Berk - 2013 - Philosophia Mathematica 21 (3):339-350.
Multi-sorted version of second order arithmetic.Farida Kachapova - 2016 - Australasian Journal of Logic 13 (5).
Coding true arithmetic in the Medvedev and Muchnik degrees.Paul Shafer - 2011 - Journal of Symbolic Logic 76 (1):267 - 288.
A System of Arithmetic in Modal Logic.Lee Merrill Davidson - 1981 - Dissertation, Yale University
Axiomatizing higher-order Kleene realizability.Jaap van Oosten - 1994 - Annals of Pure and Applied Logic 70 (1):87-111.
Undefinability vs. Definability of Satisfaction and Truth.Roman Murawski - 1999 - Vienna Circle Institute Yearbook 6:203-215.
Minimal predicates, fixed-points, and definability.Johan van Benthem - 2005 - Journal of Symbolic Logic 70 (3):696-712.
Minimal Predicates. Fixed-Points, and Definability.Johan Van Benthem - 2005 - Journal of Symbolic Logic 70 (3):696 - 712.
Arithmetic with Fusions.Jeff Ketland & Thomas Schindler - 2016 - Logique Et Analyse 234:207-226.

Analytics

Added to PP
2017-02-21

Downloads
1 (#1,769,934)

6 months
1 (#1,040,386)

Historical graph of downloads

Sorry, there are not enough data points to plot this chart.
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
Second order arithmetic and related topics.K. R. Apt & W. Marek - 1974 - Annals of Mathematical Logic 6 (3):177.

Add more references