On some aspects of measure and probability logics and a new logical proof for a theorem of Stone

One of the functions of mathematical logic is studying mathematical objects and notions by logical means. There are several important representation theorems in analysis. Amongst them, there is a well-known classical one which con cerns probability algebras. There are quite a few proofs of this result in the literature. This paper pursue two main goals. One is to consider some aspects of measure and probability logics and expose a novel proof for the mentioned representation theorem using ideas from logic and by application of an important result from model theory. The second and even more important goal is to present more connections between two fields of analysis and logic and reveal more the strength of logical methods and tools in analysis. The paper is mostly written for general mathematicians, in particular the people who are active in analysis or logic as the main audience. It is self-contained and includes all prerequisites from logic and analysis.