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(2018) The hyperuniverse project and maximality, Dordrecht, Springer.

Class forcing in class theory

Carolin Antos

pp. 1-16

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

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

Full citation:

Antos, C. (2018)., Class forcing in class theory, in C. Antos, R. Honzik, C. Ternullo & S. D. Friedman (eds.), The hyperuniverse project and maximality, Dordrecht, Springer, pp. 1-16.

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