Minimal Truth and Interpretability

Fischer, Martin H.

doi:10.1017/s1755020309990232

Cited by 14 publications

(35 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…4 Technically speaking, this formula should be written so as to distinguish the logical operations of the meta-langauge with those of the object-language. For example, using Feferman's commonly used 'dot-convention', one would write:…”

mentioning

confidence: 99%

“…FT over PA within PRA was first claimed by Halbach in [7], using cut-elimination. 16 Later, Fischer [4] gave a proof, based on the cut-elimination argument in [7], to show that PA FT is interpretable in PA. Unfortunately, a gap was discovered recently (by Fujimoto) in the cut-elimination argument in [7], which in turn impaired Fischer's interpretability claim.…”

mentioning

confidence: 99%

“…used to verify the interpretability of PA FT over PA, by using Fischer's strategy in [4]. 17 Therefore, Theorems 5.1 and 5.2 can be arrived at via two completely different routes.…”

mentioning

confidence: 99%

See 2 more Smart Citations

New Constructions of Satisfaction Classes

Enayat

Visser²

2015

Unifying the Philosophy of Truth

View full text Add to dashboard Cite

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

New Constructions of Satisfaction Classes

Enayat

Visser²

2015

Unifying the Philosophy of Truth

View full text Add to dashboard Cite

show abstract

“…Thus we may conclude It remains open, however, whether this is also the case for the truth axioms alone. Fischer, in [5], discusses a further consequence of a formalised conservativeness proof for CT. Combining this with Theorem 1.1 therefore yields Corollary 6.5.…”

Section: Approximating Sequentsmentioning

confidence: 99%

“…,k u)[g ] = F . ,N u,whence we apply Lemma 4.17 to(5) to obtain a derivation of Γ, T(F . ,N ϕ) ⇒ Δ, T(F .…”

mentioning

confidence: 99%

Conservativity for Theories of Compositional Truth via Cut Elimination

Leigh¹

2015

J. symb. log.

View full text Add to dashboard Cite

We present a cut elimination argument that witnesses the conservativity of the compositional axioms for truth (without the extended induction axiom) over any theory interpreting a weak subsystem of arithmetic. In doing so we also fix a critical error in Halbach's original presentation. Our methods show that the admission of these axioms determines a hyper-exponential reduction in the size of derivations of truth-free statements. §1. Overview. Let IΔ 0 + exp and IΔ 0 + exp 1 be the first-order theories extending Robinson's arithmetic by Δ 0 -induction and, respectively, axioms expressing the totality of the exponentiation and hyper-exponentiation function. If S is a first-order theory interpreting IΔ 0 + exp then by CT[S] we denote the extension of S by a fresh unary predicate T and the compositional axioms of truth for T. 1 In this paper we provide syntactic proofs for the following theorems.Theorem 1.1. Let S be an elementary axiomatised theory in a finite language interpreting IΔ 0 + exp. Then CT[S] conservatively extends S. Moreover, this fact is verifiable in IΔ 0 + exp 1 .Let p be a fresh unary predicate symbol not present in the language L of S. An L-formula D is an S-schema if S D → for every L-formula and there exists a finite set of formulae U such that S Dx → ∃ ϕ∈U (x = ϕ[ /p] ). Theorem 1.2. Let S be as above. For any S-schema D, the theory CT[S] + ∀x(Dx → Tx) is a conservative extension of S. Moreover, this fact is verifiable in IΔ 0 + exp 1 .The first part of Theorem 1.1 was first established by Barwise and Schlipf in the early 70s (see Theorem IV.5.3 of [1]) and later independently proved by Kotlarski, Krajewski, and Lachlan [13] for the case of S = PA, also establishing the first part of Theorem 1.2 in this case. Both proofs are model-theoretic, showing that a countable nonstandard model of S contains a full satisfaction class if it is recursively saturated. Since every model of S is elementarily extended by a recursively saturated model of the same cardinality, conservativity is obtained. Recently, Enayat and

show abstract

More on Systems of Truth and Predicative Comprehension

Nicolai

2016

Boston Studies in the Philosophy and History of Science

View full text Add to dashboard Cite

Minimal Truth and Interpretability

Cited by 14 publications

References 15 publications

New Constructions of Satisfaction Classes

New Constructions of Satisfaction Classes

Conservativity for Theories of Compositional Truth via Cut Elimination

More on Systems of Truth and Predicative Comprehension

Contact Info

Product

Resources

About