Logic Seminar: Session 7

This talk will explore a method for uniformly transforming the paradoxes of naive set theory and semantics into formal incompleteness results originally due to Georg Kreisel and Hao Wang. Dean will first trace the origins of this method in relation to Godel’s proof of the completeness theorem for first-order logic and its subsequent arithmetization by Hilbert and Bernays in their Grundlagen der Mathematik. He will then describe how the method can be applied to construct arithmetical statements formally independent of systems of set theory and second-order arithmetic via formalizations of Russell’s paradox and the Liar (and time permitting also the Skolem and Richard paradoxes). Finally, he will consider the significance of the Kreisel-Wang method with respect to both the Hilbert program and subsequent developments in set theory and reverse mathematics.

Chair for Session: tba

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