Compact spaces, elementary submodels, and the countable chain condition

Given a space X, J in an elementary submodel M of H(), define XM to be X M with the topology generated by {U M : U J M}. It is established, using anti-large-cardinals assumptions, that if XM is compact and its regular open algebra is isomorphic to that of a continuous image of some power of the two-point discrete space, then X = XM . Assuming CH+SCH (the Singular Cardinals Hypothesis) in addition, the result holds for any compact XM satisfying the countable chain condition.

• Type: Journal
• Year: 2006
• Where: APAL
• Authors: Lúcia R. Junqueira, Paul Larson, Franklin D. Tall
• Keywords: APAL 2006, Regular Open Algebra, Space X, Two-point Discrete Space