PP-2020-03: Bezhanishvili, Nick and Moraschini, Tommaso (2020) Hereditarily structurally complete intermediate logics: Citkin's theorem via Esakia duality. [Pre-print]
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Abstract
A deductive system is said to be structurally complete if its admissible rules are derivable. In addition, it is called hereditarily structurally complete if all its finitary extensions are structurally complete. In 1978 Citkin proved that an intermediate logic is hereditarily structurally complete if and only if the variety of Heyting algebras associated
with it omits five finite algebras. Despite its importance in the theory of admissible rules, a direct proof of Citkin’s theorem has never been published. In this paper we offer a selfcontained proof of Citkin’s theorem, based on Esakia duality and the method of subframe
formulas. As a corollary, we obtain a short proof of Citkin’s 2019 characterization of hereditarily structurally complete positive logics.
| Item Type: | Pre-print |
|---|---|
| Report Nr: | PP-2020-03 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2020 |
| Subjects: | Logic Mathematics |
| Depositing User: | Nick Bezhanishvili |
| Date Deposited: | 29 Jan 2020 22:40 |
| Last Modified: | 31 Jan 2020 16:46 |
| URI: | https://eprints.illc.uva.nl/id/eprint/1729 |
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