# Satisfaction Classes in Nonstandard Models of First-Order Arithmetic

@article{Engstrm2002SatisfactionCI, title={Satisfaction Classes in Nonstandard Models of First-Order Arithmetic}, author={F. Engstr{\"o}m}, journal={Mathematics eJournal}, year={2002} }

A satisfaction class is a set of nonstandard sentences respecting Tarski's truth definition. We are mainly interested in full satisfaction classes, i.e., satisfaction classes which decides all nonstandard sentences. Kotlarski, Krajewski and Lachlan proved in 1981 that a countable model of PA admits a satisfaction class if and only if it is recursively saturated. A proof of this fact is presented in detail in such a way that it is adaptable to a language with function symbols. The idea that a… Expand

#### 10 Citations

Deflationary Truth and Pathologies

- Mathematics, Computer Science
- J. Philos. Log.
- 2010

It is shown that a certain natural closure condition imposed on a satisfaction class—namely, closure of truth under sentential proofs—generates a nonconservative extension of a syntactic base theory (Peano arithmetic). Expand

A case for satisfaction classes: model theoretic vs axiomatic approaches to the notion of truth

- Mathematics
- 2013

One of the basic question we can ask about truth in a formal setting is what, if anything, we gain when we have a truth predicate at disposal. For example, does the expressive power of a language… Expand

L O ] 2 4 M ay 2 01 8 Truth , Disjunction , and Induction

- 2018

By a well-known result of Kotlarski, Krajewski, and Lachlan (1981), first-order Peano arithmetic PA can be conservatively extended to the theory CT−[PA] of a truth predicate satisfying compositional… Expand

Compositional truth with propositional tautologies and quantifier-free correctness

- Mathematics
- 2020

Cieślinski asked whether compositional truth theory with the additional axiom that all propositional tautologies are true is conservative over Peano Arithmetic. We provide a partial answer to this… Expand

Mathematisches Forschungsinstitut Oberwolfach Report No . 52 / 2006 Mini-Workshop : Logic , Combinatorics and Independence Results

- 2006

This is a collection of extended abstracts of a mini-workshop “Logic, Combinatorics and Independence results” that took place on November 25 – December 2, 2006 in Oberwolfach. The mini-workshop was… Expand

The two halves of disjunctive correctness

- Mathematics
- 2021

Ali Enayat had asked whether two halves of Disjunctive Correctness (DC) for the compositional truth predicate are conservative over Peano Arithmetic. In this article, we show that the principle… Expand

Transplendent Models: Expansions Omitting a Type

- Computer Science, Mathematics
- Notre Dame J. Formal Log.
- 2012

Two different formulations of resplendency are investigated and necessary and sufficient conditions for countable recursively saturated models of PA are proved. Expand

Interpreting the compositional truth predicate in models of arithmetic

- Computer Science, Mathematics
- Arch. Math. Log.
- 2021

We present a construction of a truth class (an interpretation of a compositional truth predicate) in an arbitrary countable recursively saturated model of first-order arithmetic. The construction is… Expand

Truth, disjunction, and induction

- Mathematics, Computer Science
- Arch. Math. Log.
- 2019

A new general form of Visser’s theorem on non-existence of infinite descending chains of truth definitions is developed by reduction to Gödel's second incompleteness theorem, rather than by using the VISSer–Yablo paradox, as in Vissers original proof. Expand

New Constructions of Satisfaction Classes

- Mathematics
- 2015

We use model-theoretic ideas to present a perspicuous and versatile method of constructing full satisfaction classes on models of Peano arithmetic. We also comment on the ramifications of our work on… Expand

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