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Class Forcing in Class Theory

In: The Hyperuniverse Project and Maximality

Author

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  • Carolin Antos

    (University of Konstanz, Zukunftskolleg/Department of Philosophy)

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 , ℭ ) $$(M,\mathcal {C})$$ 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.

Suggested Citation

  • Carolin Antos, 2018. "Class Forcing in Class Theory," Springer Books, in: Carolin Antos & Sy-David Friedman & Radek Honzik & Claudio Ternullo (ed.), The Hyperuniverse Project and Maximality, pages 1-16, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-62935-3_1
    DOI: 10.1007/978-3-319-62935-3_1
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