A useful method for obtaining alternative formulations of the analytical hierarchy

MCMP – Philosophy of Mathematics

Stanislav O. Speranski (Sobolev Institute of Mathematics) gives a talk at the MCMP Colloquium (6 November, 2014) titled "A useful method for obtaining alternative formulations of the analytical hierarchy". Abstract: In mathematical philosophy one often employs various formal systems and structures for solving philosophical tasks. In particular, many important results in Kripke's theory of truth and the like rest on definability techniques from second-order arithmetic. With this in mind, I will present one useful method for obtaining alternative formulations of the analytical hierarchy. The latter plays a key role in foundations of mathematics and theory of computation, being the generally accepted classification of undecidable problems which capture the truth predicate for first-order arithmetic of natural numbers, and whose computational complexities are less than that of second-order true arithmetic. In the course of the presentation I will mention some relevant contributions of J. Robinson, H. Putnam, J.Y. Halpern, I. Korec and others. Further applications, including those dealing with probabilistic logics, will be discussed in the final part of the talk.