Intermediate logics preserving admissible inference rules of heyting calculus
✍ Scribed by Vladimir V. Rybakov
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 767 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
The aim of this paper is to look from the point of view of admissibility of inference rules at intermediate logics having the finite model property which extend Heyting's intuitionistic propositional logic H. A semantic description for logics with the finite model property preserving all admissible inference rules for H is given. It is shown that there are continuously many logics of this kind. Three special tabular intermediate logics λ, 1 ≥ i ≥ 3, are given which describe all tabular logics preserving admissibility: a tabular logic λ preserves all admissible rules for H iff 7λ has width not more than 2 and is not included in each λ. MSC: 03B55, 03B20.