quantifier elimination

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2 total messages Started by Mahadevan Subramaniam Fri, 24 Jul 1992 15:10

#87

Author: Mahadevan Subramaniam
Date: Fri, 24 Jul 1992 15:10

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Hello,
 Can somebody point out to me references for quantifier elimination 
 over the theory of real numbers. 
  Thanks a lot in anticipation.

Re: quantifier elimination

#90

Author: H. Enderton
Date: Fri, 24 Jul 1992 22:13

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In article <1992Jul24.151022.7360@cs.albany.edu> subu@cs.albany.edu
(Mahadevan Subramaniam) writes:
> Can somebody point out to me references for quantifier elimination 
> over the theory of real numbers. 

This is in Shoenfield's book, "Mathematical Logic," page 87.
Shoenfield gives a model-theoretic proof that the theory of the
real ordered field admits elimination of quantifiers.  The
result is due to Tarski (about 1939, but not published until
after the war).  There is more recent work on upper and lower
bounds on the complexity of implementation of the decision 
procedure one gets from all this.

--Herb Enderton    (hbe@math.ucla.edu)

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