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RELATIVE UNIFICATION IN INTUITIONISTIC LOGIC: TOWARDS THE PROVABILITY LOGIC OF HA

Part of: Proof theory and constructive mathematics

Published online by Cambridge University Press:  09 October 2025

MOJTABA MOJTAHEDI
MOJTABA MOJTAHEDI*
Affiliation:
DEPARTMENT OF MATHEMATICS STATISTICS AND COMPUTER SCIENCE COLLEGE OF SCIENCES UNIVERSITY OF TEHRAN IRAN and DEPARTMENT OF MATHEMATICS WE16 GHENT UNIVERSITY GHENT BELGIUM URL: http://mmojtahedi.ir
*
E-mail: mojtahedy@gmail.com
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Abstract

This article studies relative unification and admissibility in intuitionistic logic. We generalize results of [3, 7] and prove them relative to ${\mathsf {N}}$ formulae, the class of forlmulae with No Nested Implications to the Left. The main application of this generalization is to characterize the provability logic of Heyting Arithmetic $\mathsf {HA}$ and prove its decidability [16].

Keywords

intuitionistic logicpreservativity logicadmissibility of inference rulesunification

MSC classification

Primary: 03F50: Metamathematics of constructive systems 03F99: None of the above, but in this section

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Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 41
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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