Compact spaces, elementary submodels, and the countable chain condition

Annals of Pure and Applied Logic 144 (1-3):107-116 (2006)
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Given a space in an elementary submodel M of H, define XM to be X∩M with the topology generated by . 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 in addition, the result holds for any compact XM satisfying the countable chain condition



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