Section 1 of the Appendix to Shelah’s Proper and Improper Forcing (on weak diamond), retyped with minor modifications
نویسنده
چکیده
0.1 Definition. Weak Diamond (Φ) is the statement that for every function F : 12 → 2 there exists an h : ω1 → 2 such that for all η : ω1 → 2 the set {α < ω1 | F (η α) = h(α)} is stationary. Note that by replacing h with 1 − h, Φ is equivalent to statement that for every F : 12 → 2 there exists an h : ω1 → 2 such that for all η : ω1 → 2 the set {α < ω1 | F (η α) ̸= h(α)} is stationary. Weak Diamond can be generalized to arbitrary cardinals as follows.
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