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Few questions on forcing, large cardinals
Posted:
Mar 10, 2013 8:47 PM


So isn't forcing simply Dirichlet box / pigeonhole principle? Without appeal to forcing, simply define arguments in symmetry then as to transfinite pigeonhole, what's the difference?
How can large cardinals be defined in terms of V (the Universe) when V isn't a set? How are they cardinals if they aren't of sets?
How can forcing's model be at once model and embedded in the model? Wouldn't it then be irregular?
Are there any results in recursion/computation that can't simply (or not so simply) be framed in asymptotics without appeal to transfinite cardinals?
Are there any results not of transfinite cardinals, solely due transfinite cardinals?
Thanks,
Ross Finlayson



