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Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function
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 {~ α ∈ R : p(~ α) = 0}, {~ α ∈ R : q(~ α) > 0} where p(~x), q(~x) areExpand
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The rational points of a definable set
Let $X\R^n$ be a set that is definable in an o-minimal structure over $R$. This article shows that in a suitable sense, there are very few rational points of $X$ which do not lie on some connectedExpand
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On the scheme of induction for bounded arithmetic formulas
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Provability of the Pigeonhole Principle and the Existence of Infinitely Many Primes
In this note we shall be interested in the following problems. Expand
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On the decidability of the real exponential field
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A theorem of the complement and some new o-minimal structures
The subject of o-minimality is a branch of model theory, but it has potential geometrical interest. Two excellent surveys now exist: [3] is intended for mathematical logicians while [5] is aimed atExpand
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Quasianalytic Denjoy-Carleman classes and o-minimality
We show that the expansion of the real field generated by the functions of a quasianalytic Denjoy-Carleman class is model complete and o-minimal, provided that the class satisfies certain closureExpand
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Gromov's theorem on groups of polynomial growth and elementary logic
In the fall of 1980 the authors attended Professor Tits’ course at Yale University in which he gave an account of Gromov’s beautiful proof that every finitely generated group of polynomial growth hasExpand
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