Alejandro Poveda: An invitation to the world of Prikry-type forcing

BCNSETS
BARCELONA RESEARCH GROUP IN SET THEORY
BARCELONA SET THEORY SEMINAR

An invitation to the world of Prikry-type forcing

Alejandro Poveda
Universitat de Barcelona

Abstract: Prikry-type forcing plays a central role in
combinatorics due to its close links with central set-theoretic
principles such as the Singular Cardinal Hypothesis (SCH) or the
Tree Property. The original Prikry forcing was devised to change
the cofinality of a measurable cardinal to ω, but there are now
many other more sophisticated constructions that yield more
powerful applications. Among them we can find Magidor and
Radin forcing for changing cofinalities to uncountable cardinals,
or the Diagonal supercompact Prikry forcing with collapses, due
also to Magidor, which can be used to force the failure of SCH
at the first singular cardinal. In this session we will give an
introduction from the very beginning to this family of forcings,
and if time permits we will present some easy applications.

Date: Thursday 14 February 2019
Time: 16:00
Place: Room S-1*
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Gran Via de les Corts Catalanes 585, 08007 Barcelona

* Enter the University building through the door 20 meters to the right of the
main door and, as you enter the courtyard, turn left, go to the end of the
corridor, and then downstairs.

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