Matteo Viale: Forcing and absoluteness as means to prove theorems

Monday, June 11, 2012, 16:30-18:00
Room 1.007, Mathematische Institut, Endenicher Allee 60

Speaker: Matteo Viale (University of Torino)

Title: Forcing and absoluteness as means to prove theorems

Abstract:

The forcing method has been introduced by Cohen in the early sixties to prove the independence of the continuum problem. Forcing can be presented as an “algorithm” which takes as inputs a model M of ZFC and a boolean algebra B in M and produces a boolean valued model M^B of ZFC. The first order theory of M^B depends on the first order theory of M and on the combinatorial properties of B. Since its introduction forcing has been the most powerful tool to prove independence results in set theory. In this talk we shall take a dIfferent attitude and show that forcing is a powerful tool to prove theorems in ZFC.

The talk aims to be accessible to a general audience of logicians. In particular we try to make the most part of it accessible to an audience who does not have much acquaintance with forcing.

Those interested in the argument of this seminar can consult the preprint Martin’s maximum revisited available at my web-page: http://www2.dm.unito.it/paginepersonali/viale/Martinmaximumrevisited.pdf.

If time permits I shall also sketch a proof of the main result I will present.

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