Categoricity of theories in , when κ* is a measurable cardinal. Part 2
We continue the work of [2] and prove that for λ successor, a λ-categorical theory T in is μ-categorical for every μ ≤ λ which is above the -beth cardinal.
We continue the work of [2] and prove that for λ successor, a λ-categorical theory T in is μ-categorical for every μ ≤ λ which is above the -beth cardinal.
We assume a theory T in the logic is categorical in a cardinal λ κ, and κ is a measurable cardinal. We prove that the class of models of T of cardinality < λ (but ≥ |T|+κ) has the amalgamation property; this is a step toward understanding the character of such classes of models.
We study categoricity in power for reduced models of first order logic without equality.
This paper is part II of a study on cardinals that are characterizable by a Scott sentence, continuing previous work of the author. A cardinal κ is characterized by a Scott sentence if has a model of size κ, but no model of size κ⁺. The main question in this paper is the following: Are the characterizable cardinals closed under the powerset operation? We prove that if is characterized by a Scott sentence, then is (homogeneously) characterized by a Scott sentence, for all 0 < β₁ < ω₁....
We study the notion of computable categoricity of computable structures, comparing it especially to the notion of relative computable categoricity and its relativizations. We show that every 1 decidable computably categorical structure is relatively Δ⁰₂ categorical. We study the complexity of various index sets associated with computable categoricity and relative computable categoricity. We also introduce and study a variation of relative computable categoricity, comparing it to both computable...