PP-2022-04: Bi-intermediate logics of trees and co-trees

PP-2022-04: Bezhanishvili, Nick and Martins, Miguel and Moraschini, Tommaso (2022) Bi-intermediate logics of trees and co-trees. [Pre-print]

[thumbnail of 04-BiGodel.pdf] Text

Download (378kB)


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
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

Actions (login required)

View Item View Item