Abstract. We extend Shelah’s first many model result to show that an unstable theory has 2κ many non-permutation group isomorphic models of size κ, where κ is an uncountable ...
A definition of nonstandard universe which gets over the limitation to the finite levels of the cumulative hierarchy is proposed. Though necessarily nonwellfounded, nonstandard ...
In this paper we show that the compactness of a Loeb space depends on its cardinality, the nonstandard universe it belongs to and the underlying model of set theory we live in. In...
Abstract. After small forcing, any <κ-closed forcing will destroy the supercompactness and even the strong compactness of κ. In a delightful argument, Laver [L78] proved that ...
We examine two-cardinal problems for the class of O-minimal theories. We prove that an O-minimal theory which admits some (κ, λ) must admit every (κ , λ ). We also prove that ...