Compactness, Compactification, Internal Set Theory

Zoltan Kocsis (The University of Manchester)


Compactness has several guises. It occurs in topology as a subtle analogue of finiteness, and in logic as method for constructing models of consistent sets of sentences. Some variants of compactness have enough power to "compactify" the entire mathematical universe, unlocking new forms of reasoning in an enriched "Internal" set theory. I will give a gentle introduction to Nelson's Internal Set Theory, and - time permitting - I will discuss some applications to combinatorics and real analysis. 
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