Class Forcing in Class Theory

作者: Carolin Antos

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

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

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Richard Laver, Certain very large cardinals are not created in small forcing extensions Annals of Pure and Applied Logic. ,vol. 149, pp. 1- 6 ,(2007) , 10.1016/J.APAL.2007.07.002
Carolin Antos, Sy-David Friedman, Hyperclass forcing in Morse-Kelley class theory Journal of Symbolic Logic. ,vol. 82, pp. 549- 575 ,(2017) , 10.1007/978-3-319-62935-3_2
Joel David Hamkins, Extensions with the approximation and cover properties have no new large cardinals Fundamenta Mathematicae. ,vol. 180, pp. 257- 277 ,(2003) , 10.4064/FM180-3-4