The countable existentially closed pseudocomplemented semilattice

2012/03/30 by Joël Adler, Adler, Joël
Computer Science · Mathematics · #03C05 #03C10 #03C60 #03G10 #06A12 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Rough Sets and Fuzzy Logic #math.LO #msc:03C05 #msc:03C10 #msc:03C60 #msc:03G10 #msc:06A12

paper · pdf · doi:10.48550/arxiv.1203.6700

openalex publication_date 2012/03/30 · arxiv created 2016/07/07 · arxiv updated 2016/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

As the class of pseudocomplemented semilattices is a universal Horn class generated by a single finite structure it has a ℵ₀-categorical model companion. We will construct the countable existentially closed pseudocomplemented semilattice which is the uniquely determined model of cardinality ℵ₀ of the model companion as a direct limit of algebraically closed pseudocomplemented semilattices.

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