, In addition, as |? satisfies (|?9), µ is strongly coherent We will show: (0.3) µ is CP. And finally
, Proof of (0.3) Suppose
, (|?10) was used only to show that µ is CP, which is no longer required. Note that we do not need to use (A2) in this direction
, Direction
, Direction except that in addition (A0) holds and µ is UC We show that (|?12) holds. As µ is, ),H(?) }. Direction
, V \ µ f (V) ? D. Therefore µ f is UC. Note that (A0) is not used in this direction
, Therefore f is CP, we get ? ? ? F, f (M ? ) = M ?,|?(?),H(?)
, Direction, |? satisfies (|?12)
, V \ µ f (V) ? D. Therefore µ f is UC. Note that (A0) is not used in this direction
, normal " iff it contains only conditions which are universally quantified and " apply " |? at most |F | times. More formally, Definition 35 Let F be a set and R a set of relations on P(F ) × F
, C1) cannot characterize R. Indeed, suppose the contrary, i.e. suppose
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