Weak cylindric probability algebras. (English) Zbl 0943.03054

The weak probability logic \(L_{\mathcal {AP}\forall}\) is the minimal extension of the probability logic \(L_{\mathcal {AP}}\) [see H. J. Keisler, “Probability quantifier”, in: J. Barwise et al. (eds.), Model-theoretic logics (Springer, New York), 509-556 (1985; Zbl 0587.03002)] and the infinitary logic \(L_{\mathcal A}\) [see J. Barwise, Admissible sets and structures (Springer, Berlin) (1975; Zbl 0316.02047)]. In this paper the authors introduce the notion of a locally finite-dimensional weak cylindric probability algebra as an algebraic analogue of the weak probability logic \(L_{\mathcal A\mathcal P\forall}\) and prove a kind of the corresponding representation theorem.


03G15 Cylindric and polyadic algebras; relation algebras
03B48 Probability and inductive logic
03C70 Logic on admissible sets
03C80 Logic with extra quantifiers and operators