What question did this study set out to answer?

The aim is to establish the Goldblatt-Thomason theorem for probability logic and demonstrate its applications.

July 1, 2026Open Access

Goldblatt-Thomason Theorem for Probability Logic

Key Points

The aim is to establish the Goldblatt-Thomason theorem for probability logic and demonstrate its applications.
Formulated theorems regarding probability logic with a focus on Markov processes and their structures.
Explored the definability of Harsanyi type spaces within the context of probability logic.
Developed variants of the Goldblatt-Thomason theorem for-specific subclasses of Markov processes.
The Goldblatt-Thomason theorem is successfully applied, enabling the definability of Harsanyi type spaces in probability logic.
Variants of the theorem for specific subclasses of Markov processes are obtained, enhancing the theoretical framework.
Established connections between probability logic and Markov processes, broadening understanding in the field.

Abstract

Probability logic (PL) extends propositional logic with countably many probability operators, one for each rational number between 0 and 1.The formulas of this logic are interpreted over the class of Markov processes, i.e., structures of the form ⟨Ω,Σ,T ⟩, where ⟨Ω,Σ⟩ is a measurable space and T is a Markov kernel.The main contribution of this paper is the establishment of the Goldblatt-Thomason theorem for probability logic.As an application, we show that the class of Harsanyi type spaces is definable in PL.Moreover, we obtain some variants of the Goldblatt-Thomason theorem for specific subclasses of Markov processes.

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