Recall that a subset of R is called semi-algebraic if it can be represented as a (finite) boolean combination of sets of the form {~ Î± âˆˆ R : p(~ Î±) = 0}, {~ Î± âˆˆ R : q(~ Î±) > 0} where p(~x), q(~x) areâ€¦ (More)

Press are collaborating with JSTOR to digitize, preserve and extend access to The Journal of Symbolic Logic. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover,â€¦ (More)

Let X âŠ‚ R be a set that is definable in an o-minimal expansion of R. This paper shows that, in a suitable sense, there are very few rational points of X that do not lie on some connectedâ€¦ (More)

The work in this paper has been motivated by two questions from the theory of o-minimality (see for instance [6]): (1) Does every o-minimal expansion of the real field admit analytic cellâ€¦ (More)

Drivers of soil organic carbon (SOC) storage are likely to vary in importance in different regions and at different depths due to local factors influencing SOC dynamics. This paper explores theâ€¦ (More)

We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of aâ€¦ (More)