Menachem Magidor: Some Reflections On the Continuum Hypothesis

Departmental colloquia at York University, 5/Nov/2012
3:30-4:30 pm, with refreshments at 3pm

Speaker: Menachem Magidor (HUJI)

Title: Some Reflections On the Continuum Hypothesis

Abstract: The Continuum Problem is whether there is a set of reals whose cardinality is strictly between the cardinality of the integers and the reals. This was the fi rst problem on Hilbert’s famous list and it turned out to be undecidable by the usual axiom systems for Set Theory. The results of Goedel and Cohen tell us that the axioms give very little information about the relative size of the set of integers and the set of reals. Goedel’s conjecture that strong axioms of in nity will settle the problem turned out to be false. Is this the end of the story?

In this talk we shall survey some of current approaches of trying to give a meaningful answer to the problem, in spite of its independence. Two direction of research we shall concentrate on will be forcing axioms and the theory of universally Baire sets of reals.

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