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Explore recent advances in mathematical logic through this 47-minute conference talk examining the decidability of various logical theories involving arithmetic predicates. Delve into cutting-edge research results including the undecidability of the first-order theory of integers with ordering and the Ramanujan tau function, the decidability of existential fragments in first-order theories of natural numbers with addition and exponential sequences, and the decidability of monadic second-order theories over natural numbers with ordering and exponential predicates. Gain insights into ongoing work in this specialized area of mathematical logic that bridges number theory, model theory, and computability theory, presented by a researcher actively contributing to these fundamental questions about the computational complexity of mathematical reasoning.
