On first-order theories with provability operator

Journal of Symbolic Logic 59 (4):1139-1153 (1994)
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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DOI 10.2307/2275696
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References found in this work BETA
The Predicate Modal Logic of Provability.Franco Montagna - 1984 - Notre Dame Journal of Formal Logic 25 (2):179-189.

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Citations of this work BETA
Explicit Provability and Constructive Semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.

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