ML-1998-09: A Modal Analysis of Some Principles of the Provability Logic of Heyting Arithmetic

ML-1998-09: Iemhoff, Rosalie (1998) A Modal Analysis of Some Principles of the Provability Logic of Heyting Arithmetic. [Report]

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Abstract

A Modal Analysis of some Principles of the Provability Logic of Heyting
Arithmetic
Rosalie Iemhoff

In this paper four principles and one scheme of the Provability Logic of
(intuitionistic) Heyting Arithmetic HA are studied from a modal-logical point
of view. These are, besides the well­known principles K, K4 and L of the
Provability Logic of Peano Arithmetic, the principle [](A v B) -> [](A v [] B)
and the scheme []--([]A -> V []B_i) -> []([]A -> V []B_i). Intuitionistic
modal logic is introduced. And for all principles and for the scheme
considered (seperately and together) frame completeness is proved, and the
finite model property is established.

Item Type:	Report
Report Nr:	ML-1998-09
Series Name:	Mathematical Logic and Foundations (ML)
Year:	1998
Date Deposited:	12 Oct 2016 14:40
Last Modified:	12 Oct 2016 14:40
URI:	https://eprints.illc.uva.nl/id/eprint/1398

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