[FOM] query about complexity of the theory of [R,+, < ]

John Baldwin jbaldwin at uic.edu
Mon Nov 3 14:43:13 EST 2003

At 11:01 AM 11/3/2003 -0800, Martin Davis wrote:
>A former colleague has asked me about the complexity of this theory:
>a) when R is the reals,
>b) when R is the rationals
>and has also asked whether the two are elementarily equivalent.

This these are models of the theory of divisible ordered abelian groups: it 
is complete.  In fact, as a reduct of (R, +, *,<)  we see the second
structure is o-minimal (and so the first).

Since I gave you an axiomatization the theory is decidable.  I don't know 
more refined bounds but Marker suggests there are at least exponential 
lower bounds
on the complexity.

>Information about the most recent results along these lines would be 
>FOM mailing list
>FOM at cs.nyu.edu

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