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The modal logic of Reverse Mathematics

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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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Authors and Affiliations

  1. Marshall University, 1 John Marshall Drive, Huntington, WV, 25755, USA

    Carl Mummert & Alaeddine Saadaoui

  2. U.S. Army Corps of Engineers, Washington, DC, USA

    Sean Sovine

Authors
  1. Carl Mummert
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  2. Alaeddine Saadaoui
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  3. Sean Sovine
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Correspondence to Carl Mummert.

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Mummert, C., Saadaoui, A. & Sovine, S. The modal logic of Reverse Mathematics. Arch. Math. Logic 54, 425–437 (2015). https://doi.org/10.1007/s00153-015-0417-z

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  • DOI: https://doi.org/10.1007/s00153-015-0417-z

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