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International Studies in Phenomenology and Philosophy

Book | Chapter

179389

Class forcing in class theory

Carolin Antos

pp. 1-16

Abstract

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,mathcal {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.

Publication details

Published in:

Antos Carolin, Honzik Radek, Ternullo Claudio, Friedman Sy David (2018) The hyperuniverse project and maximality. Dordrecht, Springer.

Pages: 1-16

DOI: 10.1007/978-3-319-62935-3_1

Full citation:

Antos Carolin (2018) „Class forcing in class theory“, In: C. Antos, R. Honzik, C. Ternullo & S. Friedman (eds.), The hyperuniverse project and maximality, Dordrecht, Springer, 1–16.