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Martin Sleziak
Martin Sleziak
10:19 AM
I have noticed this edit on Wikipedia, claiming that Cantor's theorem is not true for sets of cardinality $\aleph_\omega$.
Which is clearly non-sense, but it made me think what can we say about $2^{\aleph_\omega}$. I guess not much.
The study of some problems related to this is precisely the point of pcf-theory right?
PCF theory
PCF theory is the name of a mathematical theory, introduced by Saharon Shelah (1978), that deals with the cofinality of the ultraproducts of ordered sets. It gives strong upper bounds on the cardinalities of power sets of singular cardinals, and has many more applications as well. The abbreviation "PCF" stands for "possible cofinalities". == Main definitions == If A is an infinite set of regular cardinals, D is an ultrafilter on A, then we let denote the cofinality of the ordered set of functions where the ordering is defined as follows. if . pcf(A) is the set of cofinalities that occur if we...
 

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