The Topology-Free Construction of the Universal Type Structure for Conditional Probability Systems

Pierfrancesco Guarino

We construct the universal type structure for conditional probability systems without any topological assumption, namely a type structure that is terminal, belief-complete, and non-redundant. In particular, in order to obtain the belief-completeness in a constructive way, we extend the work of Meier [An Infinitary Probability Logic for Type Spaces. Israel Journal of Mathematics, 192, 1-58] by proving strong soundness and strong completeness of an infinitary conditional probability logic with truthful and non-epistemic conditioning events.

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