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On some formalized conservation results in arithmetic

P. Clote, P. Hájek & J. Paris

Archive for Mathematical Logic 30 (4):201-218 (1990)

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(1 other version)On the arithmetical content of restricted forms of comprehension, choice and general uniform boundedness.Ulrich Kohlenbach - 1998 - Annals of Pure and Applied Logic 95 (1-3):257-285.details In this paper the numerical strength of fragments of arithmetical comprehension, choice and general uniform boundedness is studied systematically. These principles are investigated relative to base systems Tnω in all finite types which are suited to formalize substantial parts of analysis but nevertheless have provably recursive functions of low growth. We reduce the use of instances of these principles in Tnω-proofs of a large class of formulas to the use of instances of certain arithmetical principles thereby determining faithfully the arithmetical (...) Download Export citation Bookmark 3 citations
Effective Bounds from ineffective proofs in analysis: An application of functional interpretation and majorization.Ulrich Kohlenbach - 1992 - Journal of Symbolic Logic 57 (4):1239-1273.details We show how to extract effective bounds Φ for $\bigwedge u^1 \bigwedge v \leq_\gamma tu \bigvee w^\eta G_0$ -sentences which depend on u only (i.e. $\bigwedge u \bigwedge v \leq_\gamma tu \bigvee w \leq_\eta \Phi uG_0$ ) from arithmetical proofs which use analytical assumptions of the form \begin{equation}\tag{}\bigwedge x^\delta\bigvee y \leq_\rho sx \bigwedge z^\tau F_0\end{equation*} (γ, δ, ρ, and τ are arbitrary finite types, η ≤ 2, G0 and F0 are quantifier-free, and s and t are closed terms). If τ (...) Download Export citation Bookmark 29 citations
Unifying the model theory of first-order and second-order arithmetic via WKL 0 ⁎.Ali Enayat & Tin Lok Wong - 2017 - Annals of Pure and Applied Logic 168 (6):1247-1283.details Download Export citation Bookmark 7 citations
Isomorphisms of Diagonalizable Algebras.V. Yu Shavrukov - 1997 - Theoria 63 (3):210-221.details Download Export citation Bookmark 1 citation
Ramsey’s theorem for pairs, collection, and proof size.Leszek Aleksander Kołodziejczyk, Tin Lok Wong & Keita Yokoyama - 2023 - Journal of Mathematical Logic 24 (2).details We prove that any proof of a [Formula: see text] sentence in the theory [Formula: see text] can be translated into a proof in [Formula: see text] at the cost of a polynomial increase in size. In fact, the proof in [Formula: see text] can be obtained by a polynomial-time algorithm. On the other hand, [Formula: see text] has nonelementary speedup over the weaker base theory [Formula: see text] for proofs of [Formula: see text] sentences. We also show that for (...) Download Export citation Bookmark
The prime number theorem and fragments ofP A.C. Cornaros & C. Dimitracopoulos - 1994 - Archive for Mathematical Logic 33 (4):265-281.details We show that versions of the prime number theorem as well as equivalent statements hold in an arbitrary model ofIΔ 0+exp. Download Export citation Bookmark 4 citations

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