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arXiv · 1401.0648

The modal logic of Reverse Mathematics

Carl Mummert·Alaeddine Saadaoui·Sean Sovine
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Abstract

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.

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Carl Mummert, Alaeddine Saadaoui, Sean Sovine. 2014-01-03. The modal logic of Reverse Mathematics. https://doi.org/10.1007/s00153-015-0417-z

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