# HYPERCLASS FORCING IN MORSE-KELLEY CLASS THEORY

@article{Antos2017HYPERCLASSFI, title={HYPERCLASS FORCING IN MORSE-KELLEY CLASS THEORY}, author={Carolin Antos and Sy-David Friedman}, journal={The Journal of Symbolic Logic}, year={2017}, volume={82}, pages={549 - 575} }

Abstract In this article we introduce and study hyperclass-forcing (where the conditions of the forcing notion are themselves classes) in the context of an extension of Morse-Kelley class theory, called MK**. We define this forcing by using a symmetry between MK** models and models of ZFC− plus there exists a strongly inaccessible cardinal (called SetMK**). We develop a coding between β-models ${\cal M}$ of MK** and transitive models M + of SetMK** which will allow us to go from ${\cal M}$ to M…

## 11 Citations

Boolean-valued class forcing

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We show that the Boolean algebras approach to class forcing can be carried out in the theory Kelley-Morse plus the Choice Scheme (KM + CC) using hyperclass Boolean completions of class partial…

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Abstract In this article I investigate the phenomenon of minimum and minimal models of second-order set theories, focusing on Kelley–Morse set theory KM, Gödel–Bernays set theory GB, and GB augmented…

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The stable core, an inner model of the form $\langle L[S],\in, S\rangle$ for a simply definable predicate $S$, was introduced by the first author in [Fri12], where he showed that $V$ is a class…

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A method of interpreting extension-talk (V-logic) is presented, and it is shown how it captures satisfaction in ‘ideal’ outer models and relates to impredicative class theories.

MODERN CLASS FORCING

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We survey recent developments in the theory of class forcing formalized in the second-order set-theoretic setting.

L O ] 1 9 Ju l 2 01 8 Universism and Extensions of V

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A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a…

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