Barcelona Logic Seminar

THE POWER OF POWER SETS OF COUNTABLE UNIONS OF COUNTABLE SETS

Asaf Karagila

Newton International Fellow, School of Mathematics, UEA (Norwich)

Date:	Wednesday, February 5.
Time:	12:30
Place:	Seminar room of the Institut de Matemàtica de la Universitat de Barcelona, School of Mathematics and Computer Science (UB). (IMUB) Gran Via 585.

Abstract

Assuming the Axiom of Choice, countable unions of countable sets are countable, and so their power sets are of size continuum. Without the Axiom of Choice, however, while countable unions of countable sets can be fairly arbitrary, in some sense we can show they are not "too large". Nevertheless, their power sets can be completely beyond control. This was shown by D.B. Morris in his Ph.D. thesis in 1970. We will not prove this theorem here, but we will discuss the broader context in which it tells us about set theory with and without the Axiom of Choice.

Supported by:

Department of Mathematics of the Universitat Politècnica de Catalunya
Department of Mathematics and Computer Science of the University of Barcelona
Department of Philosophy of the University of Barcelona
Institut de Matemàtica de la Universitat de Barcelona (IMUB)

Organized by Joan Bagaria, Enrique Casanovas and Rafel Farré

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