Mathematical Sciences: Topics in the Foundations of Mathematics

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Friedman will continue research on a number of topics that he has initiated in recent years in collaboration with other researchers, including topics in definitional structure of mathematics, reverse mathematics, algorithmic procedures, general unified proof theory, model theory of real functions, Borel reducibility for classes of countable structures, and the transferability and provability of positive sentences. Friedman also intends to explore some additional topics mostly without collaboration, including research exposition, independence results, round-off structures, Hilbert's seventeenth problem, intuitionistic set theory, foundations of ultrafinitism, and foundations of experimental mathematics.