# Alejandro Poveda: Prikry-type forcing and the failure of the Singular Cardinal Hypothesis

BCNSETS
BARCELONA RESEARCH GROUP IN SET THEORY
BARCELONA SET THEORY SEMINAR

Prikry-type forcing and the failure of the
Singular Cardinal Hypothesis

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.
In this session we will describe the Prikry forcing with collapses
and present a proof of Magidor’s theorem on the consistency,
relative to appropriate large cardinal hypotheses, of the failure
of the SCH at the first singular cardinal.

Date: Thursday 7 March 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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