Definition
The diamond principle ◊ says that there exists a ◊-sequence, in other words sets Aα⊆α for α<ω1 such that for any subset A of ω1 the set of α with A∩α = Aα is stationary in ω1.
More generally, for a given cardinal number and a stationary set, the statement ◊S (sometimes written ◊(S) or ◊κ(S)) is the statement that there is a sequence such that
- each
- for every is stationary in
The principle ◊ω1 is the same as ◊.
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