FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1996, VOLUME 2, NUMBER 2, PAGES 483-499

Grzegorczyk logic with arithmetical proof operators

E. Yu. Nogina

Abstract

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Logics with the modal operator “… is true and provable” together with the modal proof operators “p is a proof of …” are axiomatized. Kripke-style completeness, decidability and arithmetical completeness of these logics are established.

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