Undecidability of relatively free Hilbert algebras
type: Item
instance of: scholarly article
title: Undecidability of relatively free Hilbert algebras
zbMATH Open document ID: 0646.03006
DOI: 10.1007/BF01229957
author: Paweł M. Idziak
published in: Algebra Universalis
publication date: 1988-01-01T00:00:00Z
review text: Let H stand for the variety of Hilbert algebras and I for its subvariety of implication algebras. In this paper the author interprets (by a method presented by \textit{S. Burris} and \textit{R. McKenzie} [Mem. Am. Math. Soc. 246 (1981; Zbl 0483.03019)]) the class of finite partition lattices, known to have hereditarily undecidable first order theory, into a particular class of implication algebras. This class is a subclass both of the class FI of finitely generated free implication algebras and of the class of the finite members of every non-trivial variety of Hilbert algebras. Thus he proves that the above classes have hereditarily undecidable first-order theories. Also he shows that FI can be interpreted into the class FV of the finitely generated free members of every non-trivial variety of Hilbert algebras; so he derives that the first-order theories of FV's are hereditarily undecidable.
Mathematics Subject Classification ID: 03B25
Mathematics Subject Classification ID: 03C05
Mathematics Subject Classification ID: 08B20
Mathematics Subject Classification ID: 03D35
zbMATH DE Number: 4053562
zbMATH Keywords: variety of Hilbert algebras
zbMATH Keywords: implication algebras
zbMATH Keywords: finite partition lattices
zbMATH Keywords: hereditarily undecidable
reviewed by: Cornelia Kalfa
MaRDI profile type: Publication
cites work: Q5532577
cites work: Decidability and Boolean representations
cites work: Lattice-theoretic decision problems in universal algebra
cites work: Q3934450
cites work: Density and closure in implicative semi-lattices
cites work: Q3801521
cites work: Q3470450
cites work: On direct products of theories
cites work: Concatenation as a basis for arithmetic
cites work: An algebraic approach to non-classical logics
cites work: Meet-Irreducible Elements in Implicative Lattices
full work available at URL: https://doi.org/10.1007/bf01229957
OpenAlex ID: W178447142
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description: scientific article; zbMATH DE number 4053562