An analytic completeness theorem for logics with probability quantifiers

Journal of Symbolic Logic 52 (3):802-816 (1987)
Abstract
We give a completeness theorem for a logic with probability quantifiers which is equivalent to the logics described in a recent survey paper of Keisler [K]. This result improves on the completeness theorems in [K] in that it works for languages with function symbols and produces a model whose universe is an analytic subset of the real line, and whose relations and functions are Borel relative to this universe
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