Mathematical Sciences: The Foundations of Mathematics

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Simpson will continue his axiomatic studies of ordinary mathematics in the context of subsystems of second order arithmetic. Aspects of the research include: (1) Hilbert's program and functional analysis; (2) a variant of Hilbert's program based on polynomial time computability; (3) reverse mathematics in the context of countable algebra and countable combinatorics. Such studies illuminate the theoretical limits of computability and other foundational matters.