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

[Paulo Mantegazza]

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*
    *EXPOSITOR: ALEXANDRE MIQUEL*
    *(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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