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

TL;DR

This paper constructs a universal type structure for conditional probability systems without relying on topological assumptions, extending previous work with a new infinitary logic that ensures belief-completeness.

Contribution

It introduces a topology-free construction of the universal type structure, proving strong soundness and completeness of an associated infinitary logic.

Findings

Constructed a terminal, belief-complete, non-redundant type structure

Proved strong soundness and completeness of the infinitary logic

Extended Meier's work to include non-epistemic conditioning events

Abstract

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.