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Preprint Number 245
245. Misha Gavrilovich A logical construction of a model category Submission date: 3 May 2010. Abstract: (Notes of a talk given in Oxford, March
2010). Technically, we show how naive and straightforward homotopy theory style diagramme chasing leads to define a Quillen's model category of settheoretic 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 homotopyinvariant version of Generalised Continuum Hypothesis, and some similarities between PCF's and homotopy theory's ideologies. Mathematics Subject Classification: Keywords and phrases: Full text: pdf.

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