Abstract
Requiring an algebraM to be both free (for the variety it generates) and ℵ1-saturated imposes very strong conditions onM. In the simplest examples (see below) there exist a finite number of relatively free algebrasA o,...,A n-1 whose theories are ℵ1-categorical such thatM is generated (as an algebra) by the UA i In particular, this implies Th(M) has at most (α+ℵo) models of cardinality ℵα. We will show a weaker structure theorem in the general case but deduce the same constraint on the spectrum ofT.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. T.Baldwin, J.Berman, A. M. W.Glass and W.Hodges, A combinatorial fact about free algebras, (to appear).
J. T.Baldwin and R.McKenzie, Counting models in universal Horn classes.
S. Shelah,Classification Theory and the Number of Non-Isomorphic Models, North Holland, Amsterdam (1978).
Author information
Authors and Affiliations
Additional information
Dedicated to Alfred Tarski on his 80th birthday
Partially supported by N.S.F. grant 77-01667.
This research was partially supported by the United States Israel Binational Science Foundation grant 1110.
Rights and permissions
About this article
Cite this article
Baldwin, J.T., Shelah, S. The structure of saturated free algebras. Algebra Universalis 17, 191–199 (1983). https://doi.org/10.1007/BF01194528
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01194528