Comparing axiomatic theories of truth

This paper isadirect continuation of (Łełyk, Wcisło, 2017), where one particular way of comparing axiomatic theories of truth was discussed at length in the context of extensions of one concrete truth theory—the basic stratified theory of composi-tional truth, known under the name CT−. Other possible truth theories and ways of com-paring them were only briefly sketched. In the current study we want to describe this field of research in greater details. In Section 2 we shall introduce various axiomatic theories of truth. The formal definitions will be supported by intuitive explanations. In Section 3 we introduce three relations that can serve as explications of strength ofatheory. One of them will be, known from (Łełyk, Wcisło, 2017)the proof-theoretical strength, and two others, model-theoretical strength and Fujimoto definability, will be its refinements. In the last section we shall discuss the formal results showing how these relations shape the universe of theories under investigation.