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January 2020 Splittings and Disjunctions in Reverse Mathematics
Sam Sanders
Notre Dame J. Formal Logic 61(1): 51-74 (January 2020). DOI: 10.1215/00294527-2019-0032


Reverse mathematics (RM hereafter) is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson and others. The aim of RM is to find the minimal axioms needed to prove a theorem of ordinary, that is, non-set-theoretic, mathematics. As suggested by the title, this paper deals with two (relatively rare) RM-phenomena, namely, splittings and disjunctions. As to splittings, there are some examples in RM of theorems A, B, C such that A(BC), that is, A can be split into two independent (fairly natural) parts B and C. As to disjunctions, there are (very few) examples in RM of theorems D, E, F such that D(EF), that is, D can be written as the disjunction of two independent (fairly natural) parts E and F. By contrast, we show in this paper that there is a plethora of (natural) splittings and disjunctions in Kohlenbach’s higher-order RM.


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Sam Sanders. "Splittings and Disjunctions in Reverse Mathematics." Notre Dame J. Formal Logic 61 (1) 51 - 74, January 2020.


Received: 23 May 2018; Accepted: 15 January 2019; Published: January 2020
First available in Project Euclid: 18 December 2019

zbMATH: 07196092
MathSciNet: MR4054245
Digital Object Identifier: 10.1215/00294527-2019-0032

Primary: 03B30
Secondary: 03D65 , 03F35

Keywords: disjunctions , higher-order arithmetic , reverse mathematics , splittings

Rights: Copyright © 2020 University of Notre Dame


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Vol.61 • No. 1 • January 2020
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