Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-02-04T03:05:48.818Z Has data issue: false hasContentIssue false
  • English
  • Français

Large algebraic theories with small algebras

Published online by Cambridge University Press:  17 April 2009

Jan Reiterman
Jan Reiterman
Affiliation:
Faculty of Nuclear Science and Technical Engineering, Technical University of Prague, Prague, Czechoslovakia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The aim of the paper is to study the interrelation between several natural smallness conditions on an algebraic theory with a proper class of operations. The conditions concern the existence of sets of data determining algebras, homomorphisms, subalgebras, and congruences.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 3 , December 1978 , pp. 371 - 380
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Gaifman, H., “Infinite Boolean polynomials I”, Fund. Math. 54 (1964), 229–250.CrossRefGoogle Scholar
[2]Hales, A.W., “On the non-existence of free complete Boolean algebras”, Fund. Math. 54 (1964), 45–66.CrossRefGoogle Scholar
[3]Isbell, John R., “General functorial semantics, I”, Amer. J. Math. 94 (1972), 535–596.CrossRefGoogle Scholar
[4]Linton, F.E.J., “Some apsects of equational categories”, Proceedings of the Conference on Categorical Algebra, La Jolla 1965, 84–94 (Springer-Verlag, Berlin, Heidelberg, New York, 1966).CrossRefGoogle Scholar
[5]Manes, Ernest G., Algebraic theories (Graduate Texts in Mathematics, 26. Springer-Verlag, Hew York, Heidelberg, Berlin, 1976).CrossRefGoogle Scholar
[6]Reiterman, Jan, “Algebraic theories and varieties of functor algebras”, submitted.Google Scholar