Some Two-Cardinal Results for O-Minimal Theories

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 every “reasonable” variant of Chang’s Conjecture is true for O-minimal structures. Finally, we generalize these results from the two-cardinal case to the δ-cardinal case for arbitrary ordinals δ.

• Type: Journal
• Year: 1998
• Where: JSYML
• Authors: Timothy Bays
• Keywords: JSYML 1998, O-minimal, O-minimal Theories, Two-cardinal Problems