Shelah's eventual categoricity conjecture in tame abstract elementary classes with primes

Mathematical Logic Quarterly 64 (1-2):25-36 (2018)
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Abstract

A new case of Shelah's eventual categoricity conjecture is established: Let be an abstract elementary class with amalgamation. Write and. Assume that is H2‐tame and has primes over sets of the form. If is categorical in some, then is categorical in all. The result had previously been established when the stronger locality assumptions of full tameness and shortness are also required. An application of the method of proof of the mentioned result is that Shelah's categoricity conjecture holds in the context of homogeneous model theory (this was known, but our proof gives new cases): If D be a homogeneous diagram in a first‐order theory T and D is categorical in a, then D is categorical in all.

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10.1002/malq.201500068

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Citations of this work

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Universal classes near ${\aleph _1}$.Marcos Mazari-Armida & Sebastien Vasey - 2018 - Journal of Symbolic Logic 83 (4):1633-1643.

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References found in this work

Galois-stability for Tame abstract elementary classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (01):25-48.
Categoricity for abstract classes with amalgamation.Saharon Shelah - 1999 - Annals of Pure and Applied Logic 98 (1-3):261-294.
Shelah's eventual categoricity conjecture in universal classes: Part I.Sebastien Vasey - 2017 - Annals of Pure and Applied Logic 168 (9):1609-1642.
Forking and superstability in Tame aecs.Sebastien Vasey - 2016 - Journal of Symbolic Logic 81 (1):357-383.
Building independence relations in abstract elementary classes.Sebastien Vasey - 2016 - Annals of Pure and Applied Logic 167 (11):1029-1092.

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