  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.
