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An Ordering of the set of Sentences of Peano Arithmetic

Aleksandar Ignjatović (1985)

Publications de l'Institut Mathématique

Arithmetical classification of the set of all provably recursive functions

Vítězslav Švejdar (1999)

Commentationes Mathematicae Universitatis Carolinae

The set of all indices of all functions provably recursive in any reasonable theory $T$ is shown to be recursively isomorphic to $U \times \bar{U}$ , where $U$ is $Π_{2}$ -complete set.

Arithmetical transfinite induction and hierarchies of functions

Z. Ratajczyk (1992)

Fundamenta Mathematicae

We generalize to the case of arithmetical transfinite induction the following three theorems for PA: the Wainer Theorem, the Paris-Harrington Theorem, and a version of the Solovay-Ketonen Theorem. We give uniform proofs using combinatorial constructions.

Automorphisms of models of bounded arithmetic

Ali Enayat (2006)

Fundamenta Mathematicae

We establish the following model-theoretic characterization of the fragment IΔ₀ + Exp + BΣ₁ of Peano arithmetic in terms of fixed points of automorphisms of models of bounded arithmetic (the fragment IΔ₀ of Peano arithmetic with induction limited to Δ₀-formulae). Theorem A. The following two conditions are equivalent for a countable model of the language of arithmetic: (a) satisfies IΔ₀ + BΣ₁ + Exp; (b) $= I_{f i x} (j)$ for some nontrivial automorphism j of an end extension of that satisfies IΔ₀. Here $I_{f i x} (j)$ is the...

Axiomatization of the forcing relation with an application to Peano Arithmetic

Zofia Adamowicz (1984)

Fundamenta Mathematicae

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