## 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.

### MSC:

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

### Citations:

Zbl 0587.03002; Zbl 0316.02047