[FOM] Re:Clarification on Higher Set Theory

wm@cage.rug.ac.be wm at cage.rug.ac.be
Sun Feb 16 11:29:52 EST 2003

In the postings of Sean Stidd of 12 and 14 Feb and of Harvey Friedman of 13 Feb 
different ways are given to motivate belief in higher set theory.
This can be done by proving theorems using large cardinals,but unprovable in 
any other way,if these theorems are widely believed or are formulated by 
topologists within topology,etc.,(Stidd),or if it are propositions in discrete 
mathematics which reach a certain level of beauty,depth,and breadth (Friedman).
I think there is also a other way to motivate the belief in the utility of 
higher set theory.
Laver, Steel and Dehornoy have given an example where higher set theory (the 
large cardinal axiom I3, or the existence of self simular ranks) reveals new 
theorems in the theory of self distributive systems and in topology (braid 
theory), and they give proofs wich are much more beautiful and much less 
complex as any proof within the domain itself.
(see also my posting of 27 Jan: Set theory as a revealer)
I think that topologists which have studied these results are now much more 
interrested in higher set theory as before. 
However I must admit that I have no knowledge of other results of the same kind.

                Wim Mielants

Zeus Security / DSA Webmail: webmail.rug.ac.be

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