NDLI: The finite embeddability property for residuated lattices, pocrims and BCK-algebras

Content Provider	Springer Nature Link
Author	Blok, W. J. Van Alten, C. J.
Copyright Year	2002
Abstract	A class of algebras has the finite embeddability property (FEP) if every finite partial subalgebra of an algebra in the class can be embedded into a finite algebra in the class. We investigate the relationship of the FEP with the finite model property (FMP) and strong finite model property (SFMP).¶ For quasivarieties the FEP and the SFMP are equivalent, and for quasivarieties with equationally definable principal relative congruences the three notions FEP, FMP and SFMP are equivalent. The variety of intuitionistic linear algebras –which is known to have the FMP–fails to have the FEP, and hence the SFMP as well. The variety of integral intuitionistic linear algebras (also known as the variety of residuated lattices) does possess the FEP, and hence also the SFMP. Similarly contrasting statements hold for various subreduct classes. In particular, the quasivarieties of pocrims and of BCK-algebras possess the FEP. As a consequence, the universal theories of the classes of residuated lattices, pocrims and BCK-algebras are decidable.
Starting Page	253
Ending Page	271
Page Count	19
File Format	PDF
ISSN	00025240
Journal	algebra universalis
Volume Number	48
Issue Number	3
e-ISSN	14208911
Language	English
Publisher	Birkhäuser Verlag
Publisher Date	2002-10-01
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Logic Algebra and Number Theory

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The finite embeddability property for residuated lattices, pocrims and BCK-algebras