Splittings and disjunctions in Reverse Mathematics (arxiv link)

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Sam Sanders

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As suggested by the title, this paper deals with two (relatively rare) Reverse Mathematics-phenomena, namely splittings and disjunctions. As to splittings, there are some examples in RM of theorems A,B,C such that A ↔ (B ∧ C), i.e. 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 ↔ (E ∨ F), i.e. 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 Reverse Mathematics.

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The following table summarises most of the splittings and disjunctions in the paper.  The base theory for the  equivalences is always a conservative extension (for some formula class) of Kohlenbach's base theory.

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