Suppose I and my twin embark on a project. I create a mathematical system, from scratch, based on the ZFC axioms. My twin, having read the HoTT book, decides to ground his system there. Does there exist a measure to gauge how related our two systems are? How much research has been put into comparing competing formal systems, in general?
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There is an entire branch of mathematics dedicated to that. See http://en.wikipedia.org/wiki/Ordinal_analysis
Wolphram jonny
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Perfect! Thanks! – Kevin Binz Jul 03 '14 at 01:56