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7 June 2002, ILLC talks, Stefan Geschke

Speaker: Stefan Geschke (Berlin)
Title: Forcing, Elementary Substructures, and a New Axiom
Date: Friday 7 June 2002
Time: 12:00
Location: Diamantslijperij, Nieuwe Achtergracht 170, room NP.101

Abstract:

Since its introduction by Paul Cohen in 1963, forcing has become one of the most important tools, some might say the most important tool, for proving independence results relative to the Zermelo-Fraenkel system of axioms for set theory.

However, forcing remains a mystery to most people who are not experts in the field. Therefore it makes sense to isolate axioms describing the properties of certain interesting models of set theory which have been obtained by forcing. A popular example is Martin's Axiom.

We describe a general scheme for the formulation of such axioms in terms of elementary substructures of sufficiently good approximations of the set-theoretic universe. We discuss a specific example of such an "elementary submodel axiom" and show how it translates into a purely combinatorial statement about the power set of the natural numbers that does not mention any logic at all.

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