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Completeness theorem for singular biprobability models. (English) Zbl 0647.03033
The aim of the paper is to prove the completeness theorem for singular biprobability models. This also solves Keisler’s Problem 5.4 in the singular case [H. J. Keisler: “Probability quantifiers”, Model- theoretic logics, 509-556 (1985; Zbl 0587.03002)]. The case of absolute continuity is considered in an earlier paper by the author [J. Symb. Logic 51, 586-590 (1986; Zbl 0626.03031)].
03C80 Logic with extra quantifiers and operators
03B48 Probability and inductive logic
03C70 Logic on admissible sets
03H10 Other applications of nonstandard models (economics, physics, etc.)
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