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Uniqueness of limit models in classes with amalgamation
Author(s) -
Grossberg Rami,
VanDieren Monica,
Villaveces Andrés
Publication year - 2016
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201500033
Subject(s) - mathematics , cardinality (data modeling) , class (philosophy) , limit (mathematics) , uniqueness , embedding , combinatorics , discrete mathematics , embedding problem , pure mathematics , galois group , mathematical analysis , artificial intelligence , computer science , data mining
We prove the following main theorem: Let error be an abstract elementary class satisfying the joint embedding and the amalgamation properties with no maximal models of cardinality μ. Let μ be a cardinal above the the Löwenheim‐Skolem number of the class. If error is μ‐Galois‐stable, has no μ‐Vaughtian Pairs, does not have long splitting chains, and satisfies locality of splitting, then any two ( μ , σ ℓ ) ‐limits over M , for ℓ ∈ { 1 , 2 } , are isomorphic over M .