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I'm planning on attending a conference in Barcelona in September called "Large Cardinal Methods in Homotopy Theory" and want to try to be as prepared as I possibly can. Are there good references for this sort of thing other than scholarly papers (a lot of the work is stuff done by Carles Casacuberta et.al.). I'm learning a lot of large cardinals and homotopy theory already, but I'd like to understand better what is meant by "Large Cardinal Methods." Is that like... forcing? What is that?

Thanks!! Jon

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    This might not be what you're looking for but there is a link between braid groups and large cardinals. Some problems in involving braid groups were solved using large cardinals. See: http://spot.colorado.edu/~szendrei/BLAST2010/miller_new.pdf2011-08-05
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    You can also see this question: http://mathoverflow.net/questions/35281/category-and-homotopy-theoretic-methods-in-set-theory2011-08-05
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    After reading the title I immediately thought of Vopenka's principle and its uses in model theory. The best known work is due to Rosicky and Tholen which you can find easily by Googling. A very accessible source for Vopenka's principle (pun accidental) is [Adamek-Rosicky](http://books.google.com/books?id=q742EvMEKTwC) (which should be good to have at hand at that conference anyway). A more set-oriented exposition of Vopenka's principle is in Jech's [set theory](http://books.google.com/books?id=iX-UQgAACAAJ) if I remember well. Large cardinals are used for pushing the small object further.2011-08-05
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    Somehow I jumbled up my last sentence: I meant to say. Large cardinal principles can be used to push Quillen's small object argument further.... :)2011-08-16
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    I strongly suggest to find some papers in general topology or descriptive set theory in which large cardinals are used. This might give you a sense of non-consistency related proofs with large cardinals.2011-08-16

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