UNRAMIFIED F ORCING PRESERVING
Alexander Abian, Kyriakos Keremedis · 1987
Shoenfield's unramified version of Cohen's forcing is defined in two stages: one which does not preserve double negation and the other which modifies the former so as to preserve double negation. Here we express the unramified forcing, which preserves double negation, in a single stage. Surprisingly enough, the corresponding definition of forcing for equality acquires a rather simple form. In (2) forcing I~- is expressed in terms of strong forcing I~ via Pt~- Q iffp IN -t --1 Q for every formula Q of ZF set theory and every element p of a partially ordered set (P, <). In its turn, pl~Q is defined by the following five clauses: