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Preprint Number 245
245. Misha Gavrilovich
A logical construction of a model category
Submission date: 3 May 2010.
(Notes of a talk given in Oxford, March
Technically, we show how naive and straightforward homotopy theory style diagramme chasing leads to define a Quillen's model category of set-theoretic nature and show that some invariants in set theory, the covering numbers of PCF theory, are (minor variations) of left derived functors of cofibrantly replaced cardinality, in the Quillen's formalism of model categories. We suggest a homotopy-invariant version of Generalised Continuum Hypothesis, and some similarities between PCF's and homotopy theory's ideologies.
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