Exercises de style: a homotopy theory for set theory, I

Details Exercises de style: a homotopy theory for set theory, I Exercises de style: a homotopy theory for set theory, I

2011-02-28

arxiv.org/abs/1102.5562v1

Mathematics

Logic

Scientific paper

We construct a model category (in the sense of Quillen) for set theory, starting from a couple of arbitrary, but natural, conventions. This is the simplest category satisfying our conventions and modelling the notions of finiteness, countability and infinite equi-cardinality. In a subsequent paper [GH10] we give a homotopy theoretic dictionary of set theoretic concepts, most notably Shelah's covering number cov(\lambda, \aleph_1,\aleph_1, 2), recuperated from this model category. We argue that from the homotopy theory point of view our construction is, essentially, automatic following basic existing methods, and so is (almost all) the verification that the construction works.

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