Skip to main content
SpringerLink
Log in

Union decompositions and universal classes categorical in power

  • Published:
algebra universalis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • Burris, S. N. [71]Models in equational theories of unary algebras. Algebra Universalis, vol.1 (1971), pp. 386–392.

    Article  MathSciNet  Google Scholar 

  • Chang, C. C. [68]Some remarks on model theory of infinitary languages. The Syntax and Semantics of Infinitary Languages, Lecture Notes in Mathematics, vol. 72, ed. J. Barwise, Springer-Verlag, Berlin, 1968, pp. 36–63.

    Google Scholar 

  • Chang, C. C. andKeisler, H. J. [73] Model Theory, North-Holland Publishing Co., Amsterdam, 1973, xii+550 pp.

    MATH  Google Scholar 

  • Ehrenfeucht, A. andMostowski, A. [56]Models of axiomatic theories admitting automorphisms. Fund. Math., vol.43 (1956), pp. 50–68.

    MATH  MathSciNet  Google Scholar 

  • Givant, S. R. [72]Universal relational theories. Notice Amer. Math. Soc., vol.19 (1972), p. A-603.

    Google Scholar 

  • — [73]A union decomposition theorem for unary algebras and an application to certain theories categorical in power, Notices Amer. Math. Soc., vol.20 (1973), p. A-445.

    Google Scholar 

  • — [75]A complete representation theorem for varieties categorical in power. Notices Amer. Math. Soc., vol.22 (1975), pp. A-33, A-34.

    Google Scholar 

  • — [78]Universal Horn classes categorical or free in power. Annals Math. Logic, vol.15 (1978), pp. 1–53.

    Article  MATH  MathSciNet  Google Scholar 

  • Grätzer, G. [68] Universal Algebra, D. Van Nostrand Co., Inc., Princeton, 1968, xvi+368 pp.

  • Jónsson, B. [72] Topics in Universal Algebra, Lecture Notes in Mathematics, vol.250, Springer-Verlag, Berlin, 1972, vi+220 pp.

    MATH  Google Scholar 

  • Marsh, W. [66] On ω1-categorical but not ω-categorical Theories. Doctoral dissertation, Dartmouth College, Hanover, 1966, 21 pp.

    Google Scholar 

  • Morley, M. andVaught, R. [62]Homogeneous universal models. Math. Scand., vol.11 (1962), pp. 37–57.

    MATH  MathSciNet  Google Scholar 

  • Palyutin, E. A. [71]Modeli so schetno-kategorichnymi universal'nymi teorijami. Algebra i Logika, vol.10 (1971), pp. 23–32. (English translation:Models with countable-categorical universal theories. Algebra and Logic, vol.10 (1972), pp. 15–20.)

    MATH  MathSciNet  Google Scholar 

  • Sacks, G. E. [72] Saturated Model Theory, W. A. Benjamin, Inc., Reading, 1972, xii+335 pp.

    MATH  Google Scholar 

  • Tarski, A. [54]Contributions to the theory of models. I, II. Nederl. Akad. Wetensch. Proc. Ser. A, vol. 57 (Indag. Math., vol. 16) (1954), pp. 572–588.

    MathSciNet  Google Scholar 

  • — [56] Ordinal Algebras, with appendices by C. C. Chang and B. Jónsson North-Holland Publishing Co., Amsterdam, 1956, vi+133 pp.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of California, Berkeley, California, USA

    Steven Givant

Authors
  1. Steven Givant
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The results reported in this paper constitute the second part of my doctoral dissertation, written at the University of California, Berkeley, under the direction of Professor Robert L. Vaught. I should like to express here my gratitude to Professor Vaught for the many hours he spent with me discussing my results and for the invaluable suggestions he made. The paper was prepared for publication while the author was working on a research project sponsored by the National Science Foundation, grant number MCS77-22913.

I am indebted to the referee for several very helpful suggestions. In particular, he pointed out an error in the formulation of a lemma, and indicated an easy way of avoiding the lemma altogether.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Givant, S. Union decompositions and universal classes categorical in power. Algebra Universalis 10, 155–175 (1980). https://doi.org/10.1007/BF02482899

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02482899

Keywords

Search

Navigation