Class-Forcing in Class Theory

Carolin Antos

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arXiv · 1503.00116

Class-Forcing in Class Theory

Carolin Antos

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Abstract

In this article we adapt the existing account of class-forcing over a ZFC model to a model $(M,\mathcal{C})$ of Morse-Kelley class theory. We give a rigorous definition of class-forcing in such a model and show 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.

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BibTeX RIS

Carolin Antos. 2015-02-28. Class-Forcing in Class Theory. https://arxiv.org/abs/1503.00116

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