Finite Lattices Generating Not Finitely–Based and Nonstandard Quasivarieties

2025

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DOI 10.1155/jom/1518160
Data confidence 70 medium
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Abstract

There are two well‐known and closely related problems in lattice theory: Which finite lattices generate finitely‐based quasivarieties? and Which finite lattices generate standard quasivarieties? The main goal of the paper is to contribute to both problems. The sufficient conditions under which a given lattice quasivariety is neither finitely axiomatizable nor standard. Based on these conditions, numerous examples of finite lattices generating such quasivarieties are presented.