[Todos CMAT] Reunión del Grupo de Trabajo de Álgebra y temas afines. Martes 19 de Noviembre

Paulo Mantegazza paulo en cmat.edu.uy
Jue Nov 14 10:35:37 UYST 2013

Reunión del Grupo de Trabajo de Álgebra y temas afines.
Horario 15/16.
Salon de Seminarios del piso 15
Martes 19 de Noviembre
*An axiomatic presentation of forcing*
*(la exposición será en inglés)*

The method of forcing was introduced by Cohen in 1963 to prove the
relative consistency of the negation of the Continuum Hypothesis
with respect to the axioms of ZFC.  Since the relative consistency
of the Continuum Hypothesis w.r.t. the axioms of ZFC was already
proved by Gödel in 1938, Cohen's result gave a definitive answer
to Hilbert's 1st problem.  After Cohen's achievement, the method of
forcing quickly brought further independence results in set theory,
and became an invaluable tool in the study of large cardinals.

Traditionally, forcing is presented as a model transformation, that
takes a given model M of ZF (the ground model) and builds a larger
model M[G], called a generic extension of M.  In this talk, I will
show that forcing can be seen as a _theory transformation_ as well,
that is: as a transformation taking a particular axiomatization T
of set theory (describing some ground model) and building a new
axiomatization T^* of set theory (describing the corresponding
generic extension). As we shall see, the transformation T -> T*
is surprisingly simple (the axioms of T^* are deduced from those
of T using a very simple algorithm), while hiding most technical
details of the underlying model-theoretic construction - which
makes this presentation well-suited for the "end user".

-- Alexandre Miquel (Fing/Equipo de Lógica)

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