Abstract. A set theoretical assertion ψ is forceable or possible, written ♦ ψ, if ψ holds in some forcing extension, and necessary, written ψ, if ψ holds 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.
In our previous paper REF , we introduced the modal logic of forcing and proved that the ZFC-provably valid principles of forcing were exactly those in the modal theory known as S4.2.
THE MODAL LOGIC OF FORCING
Transactions of the American Mathematical Society
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