The structure of saturated free algebras

J. T. Baldwin*, S. Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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 languageEnglish
Pages (from-to)191-199
Number of pages9
JournalAlgebra Universalis
Volume17
Issue number1
DOIs
StatePublished - Dec 1983

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