Categoricity, amalgamation, and tameness

By J. Baldwin, Alexei S. Kolesnikov. 2009

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AbstractTheorem: For each 2 ≤ k < ω there is an $$ L_{\omega _1 ,\omega } $$-sentence ϕk such that(1) ϕk is categorical in μ if μ≤ℵk−2;(2) ϕk is not ℵk−2-Galois stable(3) ϕk is not categorical in any μ with μ>ℵk−2;(4) ϕk has the disjoint amalgamation property(5) For k > 2 (a) ϕk is (ℵ0, ℵk−3)-tame; indeed, syntactic first-order types determine Galois types over models of cardinality at most ℵk−3; (b) ϕk is ℵm-Galois stable for m ≤ k − 3 (c) ϕk is not (ℵk−3, ℵk−2).

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/71a0fbfe924244af02f75de090935f54e1afb608