Peter Holy: The exact strength of the class forcing theorem

Monday, October 23, 2017, 16.30
Seminar room 0.008, Mathematical Institute, University of Bonn

Speaker: Peter Holy (Universität Bonn)

Title: The exact strength of the class forcing theorem


We consider second order set theories, that have as objects both sets and classes, and the role of the class forcing theorem, that is the forcing theorem for all notions of class forcing, within this range of theories. While Kelley-Morse class theory (KM) proves the class forcing theorem, its failure is consistent with the axioms of Gödel-Bernays set theory (GBC). We show that the class forcing theorem is equivalent, over GBC, to the principle of elementary transfinite (class) recursions of length Ord, and to the existence of various kinds of truth predicates. This is joint work with Victoria Gitman, Joel Hamkins, Philipp Schlicht and Kameryn Williams.

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