# 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}
}
• Published 14 October 2015
• Mathematics, Computer Science
• The Journal of Symbolic Logic
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…
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