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The modal logic of forcing

By Joel David, Hamkins and Benedikt L Öwe


Abstract. A set theoretical assertion ψ is forceable or possible, written ♦ ψ, if ψ holds in some forcing extension, and necessary, written□ψ, ifψholds in all forcing extensions. In this forcing interpretation of modal logic, we establish that if ZFC is consistent, then the ZFC-provable principles of forcing are exactly those in the modal theory S4.2. 1

Year: 2013
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