Preservation of Properness under Countable Support Iteration
نویسنده
چکیده
If ≤ is a preorder on a set P and p0 ≤ p1, we say that p1 is an extension of p0. Recall that a preorder is separative if and only if whenever p1 is not an extension of p0 there is an extension of p1 which is incompatible with p0. We say that P = (P,≤) is a forcing notion (also forcing poset) if ≤ is a separative preorder with minimal element 0P. Note that if P is separative and p1 p̌0 ∈ Ġ then p0 ≤ p1 (here Ġ is the canonical name of the P-generic set). Also often in forcing formulas we write a instead of ǎ for an element a of the ground model V .
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