The absorption law: Or: how to Kreisel a Hilbert–Bernays–Löb

Archive for Mathematical Logic 60 (3-4):441-468 (2020)
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Abstract

In this paper, we show how to construct for a given consistent theory U a $$\varSigma ^0_1$$ Σ 1 0 -predicate that both satisfies the Löb Conditions and the Kreisel Condition—even if U is unsound. We do this in such a way that U itself can verify satisfaction of an internal version of the Kreisel Condition.

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2021

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10.1007/s00153-020-00752-5

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References found in this work

Mathematical logic.Willard Van Orman Quine - 1951 - Cambridge,: Harvard University Press.
Solution of a problem of Leon Henkin.M. H. Löb - 1955 - Journal of Symbolic Logic 20 (2):115-118.
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Arithmetization of Metamathematics in a General Setting.Solomon Feferman - 1960 - Journal of Symbolic Logic 31 (2):269-270.
On the scheme of induction for bounded arithmetic formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (C):261-302.

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