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The modal logic of reverse mathematics. (English) Zbl 1369.03102

Summary: The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to formalize the logic of Reverse Mathematics into a system that we name s-logic. We argue that s-logic captures precisely the “logical” content of the implication and nonimplication relations between subsystems in Reverse Mathematics. We present a sound, complete, decidable, and compact tableau-style deductive system for s-logic, and explore in detail two fragments that are particularly relevant to Reverse Mathematics practice and automated theorem proving of Reverse Mathematics results.

MSC:

03B30 Foundations of classical theories (including reverse mathematics)
03B45 Modal logic (including the logic of norms)
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