Philosophy Forcing

  • Department of Philosophy
    Antos, Carolin (2018): Class Forcing in Class Theory ANTOS, Carolin, ed., Sy-David FRIEDMAN, ed., Radek HONZIK, ed., Claudio TERNULLO, ed.. The hyperuniverse project and maximality. Cham: Birkhäuser, 2018, pp. 1-16. ISBN 978-3-319-62934-6. Available under: doi: 10.1007/978-3-319-62935-3_1

Class Forcing in Class Theory


In this article we show that Morse-Kelley class theory (MK) provides us with an adequate framework for class forcing. We give a rigorous definition of class forcing in a model (M,C) of MK, the main result being that the Definability Lemma (and the Truth Lemma) can be proven without restricting the notion of forcing. Furthermore we show under which conditions the axioms are preserved. We conclude by proving that Laver’s Theorem does not hold for class forcings.

Origin (projects)

Funding sources
Name Finanzierungstyp Kategorie Project no.
Sonstige EU third-party funds research funding program 554/17
Further information
Period: 01.04.2017 – 31.03.2019