Cardinalité, saturation et finitude
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.
Categoricity of theories in Lκω , when κ is a measurable cardinal. Part 1
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.
Čech-Stone remainders of spaces that look like
Comments on Ultraproducts of Forcing Systems
Compactness of Powers of ω
We characterize exactly the compactness properties of the product of κ copies of the space ω with the discrete topology. The characterization involves uniform ultrafilters, infinitary languages, and the existence of nonstandard elements in elementary extensions. We also have results involving products of possibly uncountable regular cardinals.