Stable structures homogeneous for a finite binary language

Alistair H. Lachlan*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

Let L be a finite relational language and H(L) denote the class of all countable stable L-structures M for which Th(M) admits elimination of quantifiers. For M ∈H(L) define the rank of M to be the maximum value of CR(p, 2), where p is a complete 1-type over Ø and CR(p, 2) is Shelah's complete rank. If L has only unary and binary relation symbols there is a uniform finite bound for the rank of M ∈H(L). This theorem confirms part of a conjecture of the first author. Intuitively it says that for each L there is a finite bound on the complexity of the structures in H(L).

Original languageEnglish
Pages (from-to)155-180
Number of pages26
JournalIsrael Journal of Mathematics
Volume49
Issue number1-3
DOIs
StatePublished - Sep 1984

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