PP-2022-04: Bezhanishvili, Nick and Martins, Miguel and Moraschini, Tommaso (2022) Bi-intermediate logics of trees and co-trees. [Pre-print]
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Abstract
A bi-Heyting algebra validates the Go ̈del-Dummett axiom (p → q) ∨ (q → p) iff the poset of its prime filters is a disjoint union of co-trees (i.e., order duals of trees). Bi-Heyting algebras of this form are called bi-Go ̈del algebras and form a variety that algebraizes the extension bi-LC of bi-intuitionistic logic axiomatized by the Go ̈del-Dummett axiom. In this paper we initiate the study of the lattice Λ(bi-LC) of extensions of bi-LC. We develop the method of Jankov formulas for bi-Go ̈del algebras and use them to prove that Λ(bi-LC) has the size of the continuum. We also show that bi-LC is not locally tabular and give a criterion of locall tabularity in Λ(bi-LC).
| Item Type: | Pre-print |
|---|---|
| Report Nr: | PP-2022-04 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2022 |
| Subjects: | Logic Mathematics |
| Depositing User: | Nick Bezhanishvili |
| Date Deposited: | 05 Apr 2022 22:59 |
| Last Modified: | 05 Apr 2022 22:59 |
| URI: | https://eprints.illc.uva.nl/id/eprint/1877 |
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