Reducibility

[Russ Abbott <russ.abbott@gmail.com>]

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
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   blog: http://russabbott.blogspot.com/
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