Abstract
Requiring an algebra M to be both free (for the variety it generates) and א1-saturated imposes very strong conditions on M. In the simplest examples (see below) there exist a finite number of relatively free algebras Ao,..., An-1 whose theories are א1-categorical such that M is generated (as an algebra) by the U Ai 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 of T.
Original language | English |
---|---|
Pages (from-to) | 191-199 |
Number of pages | 9 |
Journal | Algebra Universalis |
Volume | 17 |
Issue number | 1 |
DOIs | |
State | Published - Dec 1983 |