Transfering saturation, the finite cover property, and stability

John T. Baldwin*, Rami Grossberg, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Saturation is (μ , κ)-transferable in T if and only if there is an expansion T1, of T with |T1| = |T| such that if M is a μ-saturated model of T1 and |M| ≥ κ then the reduct M|L(T) is κ-saturated. We characterize theories which are superstable without f.c.p., or without f.c.p. as, respectively those where saturation is (א0, λ)-transferable or (κ(T), λ)-transferable for all λ. Further if for some μ ≥ \T\, 2μ >+, stability is equivalent to fo: all μ ≥ |T|, saturation is (μ, 2μ)-transferable.

Original languageEnglish
Pages (from-to)678-684
Number of pages7
JournalJournal of Symbolic Logic
Volume64
Issue number2
DOIs
StatePublished - Jun 1999

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