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

A. Visser

doi:10.1007/s00153-020-00752-5

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

A. Visser

OFR - Theoretical Philosophy Emeriti

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

In this paper, we show how to construct for a given consistent theory U a Σ01-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.

Original language	English
Pages (from-to)	441–468
Journal	Archive for Mathematical Logic
Volume	60
Early online date	16 Dec 2020
DOIs	https://doi.org/10.1007/s00153-020-00752-5
Publication status	Published - 2021

Keywords

Provability
Arithmetization
incompleteness

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s00153-020-00752-5Final published version, 438 KBLicence: CC BY

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title = "The absorption law: Or: how to Kreisel a Hilbert–Bernays–L{\"o}b",

abstract = "In this paper, we show how to construct for a given consistent theory U a Σ01-predicate that both satisfies the L{\"o}b 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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AB - In this paper, we show how to construct for a given consistent theory U a Σ01-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.

KW - Provability

KW - Arithmetization

KW - incompleteness

U2 - 10.1007/s00153-020-00752-5

DO - 10.1007/s00153-020-00752-5

M3 - Article

SN - 0933-5846

VL - 60

SP - 441

EP - 468

JO - Archive for Mathematical Logic

JF - Archive for Mathematical Logic

ER -

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

Abstract

Keywords

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