The Absorption Law, or How to Kreisel a Hilbert-Bernays-L\"ob

DOI10.1007/S00153-020-00752-5arXiv1804.07465WikidataQ114852532 ScholiaQ114852532MaRDI QIDQ6300579

Albert Visser

Publication date: 20 April 2018

Abstract: In this paper, we show how to construct for a given consistent theory $U$ a $Sigm{a}_1^0$-predicate that both satisfies the L"ob 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.

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Provability logics and related algebras (e.g., diagonalizable algebras) (03F45) Gödel numberings and issues of incompleteness (03F40)

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