The question as posed makes no sense. To begin with, there are too many groups to form a set, so you need to pose this as a question about classes rather than sets, and f needs to map classes instead of sets. Second, you must first specify a larger class of which the class of all groups is a proper subclass. Otherwise what does it mean for x not to be a member of A? In this case, what does it mean not to be a group? If you make the larger class "everything" then f has an unmanageably large domain. What if you apply f to an anteater, for example? Vaughan Pratt On 7/19/2010 9:46 AM, Russ Abbott wrote:
Hi,
I apologize if this is off topic. I'm not sure where to direct this question.
I'm interested in when one can say that one theory is reducible to another. Reducibility is defined: a set A is T-reducible to a set B if there is a function f of type T such that x is a member of A if and only if f(x) is a member of B. Mathematical groups are defined in terms of a 0 element, other elements, and an operation with certain properties. Let A be the set of mathematical groups (set of models of groups?). Is there an interesting set B and function type T so that A is T-reducible to B?
First of all, is that an interesting question to ask? If so, how would one go about thinking about it?
Thanks for any help or pointers you can give me.
-- Russ Abbott ______________________________________
Professor, Computer Science California State University, Los Angeles
cell: 310-621-3805 Google voice: 424-2Blue4 blog: http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ ______________________________________
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