Mathematical Sciences: Set Theory

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This project deals with various aspects of set theory. These include: (i) the study of the structure of definable sets of reals and the role of strong hypotheses like the axiom of definable determinacy and the existence of large cardinals, as well as their mutal interrelationships, (ii) problems in combinatorial set theory and forcing and (iii) applications of set theoretic ideas and techniques to analysis. Three investigators will be involved: A.S. Kechris, W.H. Woodin, B. Velickovic, as well as several students.