A Boolean Model of Ultra lters
نویسنده
چکیده
We introduce the notion of Boolean measure algebra. It can be described shortly using some standard notations and terminology. If B is any Boolean algebra, let B N denote the algebra of sequences (xn); xn 2 B: Let us write p k 2 B N the sequence such that p k (i) = 1 if i k and p k (i) = 0 if k < i: If x 2 B, denote by x 2 B N the constant sequence x = (x; x; x; : : :): We deene a Boolean measure algebra to be a Boolean algebra B with an operation : B N ! B such that (p k) = 0 and (x) = x. Any Boolean measure algebra can be used to model non principal ultraalters in a suitable sense. Also, we can build eeectively the initial Boolean measure algebra. This construction is related to the closed open Ramsey Theorem 8].
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