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Unification and projectivity in Fregean varieties

2010/12/04 by Katarzyna Słomczyńska, Słomczyńska, Katarzyna
Computer Science · Mathematics · #03G25 #06D20 (Secondary) #08B30 (Primary) #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #math.LO #msc:03G25 #msc:06D20 #msc:08B30

paper · pdf · doi:10.48550/arxiv.1012.0937

21 pages

arxiv created 2010/12/04 · openalex publication_date 2010/12/04 · arxiv updated 2010/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In some varieties of algebras one can reduce the question of finding most general unifiers (mgus) to the problem of the existence of unifiers that fulfill the additional condition called projectivity. In this paper we study this problem for Fregean (1-regular and orderable) varieties that arise from the algebraization of fragments of intuitionistic or intermediate logics. We investigate properties of Fregean varieties, guaranteeing either for a given unifiable term or for all unifiable terms, that projective unifiers exist. We indicate the identities which fully characterize congruence permutable Fregean varieties having projective unifiers. In particular, we show that for such a variety there exists the largest subvariety that have projective unifiers.

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