Categoricity

Rami Grossberg
... classes, and is part of the active effort to prove two of Saharon Shelah's outstanding categoricity conjectures Conjecture 1 ... (Categoricity for ) ... (Categoricity for AECs) See and ...

Morley's Categoricity Theorem - History and Motivation
... immediately led to the more subtle notion of κ-categoricity, which asks for which cardinals κ is there exactly one model of cardinality κ of the given theory T up ... in all the cases he could think of, κ-categoricity at any one uncountable cardinal implied κ-categoricity at all other uncountable cardinals ...

Model Theory - Categoricity
... But two famous model-theoretic theorems deal with the weaker notion of κ-categoricity for a cardinal κ ... It turns out that the question of κ-categoricity depends critically on whether κ is bigger than the cardinality of the language (i.e ... A few characterizations of -categoricity include For a complete first-order theory T in a finite or countable signature the following conditions are equivalent T is -catego ...