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LFCS Seminar: Alberto Policriti

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The decidability of the Bernays-Schoenfinkel-Ramsey class in Set Theory

  • LFCS Seminar
When Jun 12, 2012
from 04:00 PM to 05:00 PM
Where IF 4.31-4.33
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In this talk I will describe the set-theoretic version of the Classical Decision Problem for First Order Logic. I will then illustrate the result on the decidability of the class of purely universal formulae on the unquantified language whose relational symbols are membership and equality. The class we studied is, in the classical (first order) case, the so-called Bernays-Schoenfinkel-Ramsey (BSR) class.

The set-theoretic decision problem calls for the existence of an algorithm that, given a purely universal formula in membership and equality, establishes whether there exist sets that substituted for the free variables will satisfy the formula. The sets to be used are pure sets, namely sets whose only elements are sets.

Much of the difficulties in solving the decision problem for the BSR class in Set Theory came from the ability to express infinity in it, a proprety not shared by the classical BSR class. The result makes use of a set-theoretic version of the argument Ramsey used to characterize the spectrum of the BSR class in the classical case. This characterization was the result that motivated Ramsey celebrated combinatorial theorem.

This is joint work with E. Omodeo.
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