On first-order theories with provability operator

Journal of Symbolic Logic 59 (4):1139-1153 (1994)
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Abstract

In this paper the modal operator "x is provable in Peano Arithmetic" is incorporated into first-order theories. A provability extension of a theory is defined. Presburger Arithmetic of addition, Skolem Arithmetic of multiplication, and some first order theories of partial consistency statements are shown to remain decidable after natural provability extensions. It is also shown that natural provability extensions of a decidable theory may be undecidable

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Sergei Artemov
CUNY Graduate Center

Citations of this work

Explicit provability and constructive semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
Provability logic.Rineke Verbrugge - 2008 - Stanford Encyclopedia of Philosophy.
Explicit provability and constructive semantics. [REVIEW]Jeremy D. Avigad - 2002 - Bulletin of Symbolic Logic 8 (3):432-432.

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References found in this work

Computability and Logic.George S. Boolos, John P. Burgess & Richard C. Jeffrey - 2003 - Bulletin of Symbolic Logic 9 (4):520-521.
Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
The Unprovability of Consistency. An Essay in Modal Logic.C. Smoryński - 1979 - Journal of Symbolic Logic 46 (4):871-873.
The predicate modal logic of provability.Franco Montagna - 1984 - Notre Dame Journal of Formal Logic 25 (2):179-189.

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