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Preprint Number 1104
1104. Sebastien Vasey
Shelah's eventual categoricity conjecture in universal classes. Part I
E-mail: sebv at cmu dot edu
The proof stems from ideas of Adi Jarden and Will Boney, and also relies
on a deep result of Shelah. As opposed to previous works, the argument
is in ZFC and does not use the assumption of categoricity in a successor
cardinal. The argument generalizes to abstract elementary classes (AECs)
that satisfy a locality property and where certain prime models exist.
Moreover assuming amalgamation we can give an explicit bound on the Hanf
number and get rid of the cofinality restrictions:
Mathematics Subject Classification: 03C48 (Primary), 03C45, 03C52, 03C55 (Secondary)
Keywords and phrases: Abstract elementary classes; Categoricity; Amalgamation; Forking; Independence; Classification theory; Superstability; Universal classes; Intersection property; Prime models.
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