Abstract
New examples of varieties with no nontrivial finite members given in this paper improve some earlier results or answer some open questions in this area. In particular, a generalization of Marczewski’s problem presented at the International Algebra Conference in Lisbon, June 88, is shown to have a solution in the negative.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A.K. Austin, [1965], A note on models of identities, Proc. Amer. Math. Soc. 16, 522–523.
A.K. Austin, [1966], Finite models for laws in two variables, Proc. Amer. Math. Soc. 17, 1410–1412.
S. Burris, [1972], Models in equational theories of unary algebras, Algebra Universalis 1, 386–392.
J. Dudek, [1982], On the variety V ∞ (+, 0), Math. Sem. Notes 10, 9–15.
J. Dudek, [1985], Polynomially infinite varieties of algebras I, Math. Inst. Univ. Wroclaw, Preprint no 30.
J. Dudek, [1988], A note on models of identities, Algebra Universalis, 25, 400-401.
J. Dudek and A. Kisielewicz, [a], On finite models of regular identities, Notre Dame J. Formal Logic, to appear.
A. Goetz and C. Ryll-Nardzewski, [1960], On bases of abstract algebras, Bull. Acad. Pol. Sci., Sér. Sci. Math. Astr. Phys. 8, 157–161.
G. Grätzer, [1967], On spectra of classes of universal algebras, Proc. Amer. Math. Soc. 18, 729–735.
G. Grätzer, [1979], Universal Algebra, 2nd ed., Springer-Verlag, Berlin.
B. Jonsson and A. Tarski, [1961], On two properties of free algebras, Math. Scand. 9, 95–101.
A. Kisielewicz, [1988], Marczewsk’s problem on algebras with bases of different cardinalities — solution and generalization, Bull. Acad. Pol. Sci., Sér. Sci. Math. Astr. Phys., to appear.
A. Kisielewicz, [a], On algebras with bases of different cardinalities, Fund. Math., to appear.
R. McKenzie, [1975], On spectra, and the negative solution of the decision problem for identities having a finite non-trivial model, J. Symbolic Logic 40, 186–196.
S.K. Stein, [1965], Finite models of identities, Proc. Amer. Math. Soc. 14, 216–222.
W. Taylor, [1973], Characterizing Mal’cev conditions, Algebra Universalis 3, 351–397.
W. Taylor, [1979], Equational Logic, Houston J. Math., survey iss.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer Science+Business Media New York
About this chapter
Cite this chapter
Kisielewicz, A. (1990). Varieties of Algebras with no Nontrivial Finite Members. In: Almeida, J., Bordalo, G., Dwinger, P. (eds) Lattices, Semigroups, and Universal Algebra. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2608-1_14
Download citation
DOI: https://doi.org/10.1007/978-1-4899-2608-1_14
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-2610-4
Online ISBN: 978-1-4899-2608-1
eBook Packages: Springer Book Archive