A continuum of incomplete intermediate logics
Tadeusz Litak
TL;DR
This paper extends the study of intermediate logics by constructing a continuum of Kripke incomplete logics, correcting previous proofs and broadening the understanding of logical incompleteness.
Contribution
It introduces a continuum of Kripke incomplete intermediate logics and corrects a previous proof error, advancing the theoretical landscape.
Findings
Constructed a continuum of Kripke incomplete intermediate logics
Corrected an error in the original proof of Shehtman's logic
Expanded the class of known incomplete intermediate logics
Abstract
This paper generalizes the 1977 paper of V.B. Shehtman, which constructed the first Kripke incomplete intermediate logic, by presenting a continuum of such logics. This version fixes an error in my simplified proof of incompleteness of Shehtman's original logic.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Advanced Algebra and Logic · Logic, programming, and type systems