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JOURNALS // Algebra i logika // Archive
Algebra Logika, 2016 Volume 55, Number 4, Pages 493–497 (Mi al755)
The class of bounded lattices is not axiomatizable

M. V. Schwidefskyab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia

Abstract: We prove that the class of bounded (lower bounded, upper bounded) lattices is not closed under ultraproducts, thereby solving an open problem.

Keywords: axiomatizable class, lower bounded lattice, free lattice, ultraproduct.

UDC: 512.56

Received: 07.12.2015

DOI: 10.17377/alglog.2016.55.408


 English version: Algebra and Logic, 2016, 55:4, 327–329

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© Steklov Math. Inst. of RAS, 2026