Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function

@article{Wilkie1996ModelCR,
  title={Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function},
  author={A. Wilkie},
  journal={Journal of the American Mathematical Society},
  year={1996},
  volume={9},
  pages={1051-1094}
}
  • A. Wilkie
  • Published 1996
  • Mathematics
  • Journal of the American Mathematical Society
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) are n-variable polynomials with real coefficients. A map from R to R is called semi-algebraic if its graph, considered as a subset of R, is so. The geometry of such sets and maps (“semi-algebraic geometry”) is now a widely studied and flourishing subject that owes much to the foundational work in the… Expand
406 Citations
The real field with an irrational power function and a dense multiplicative subgroup
  • 1
  • PDF
On the decidability of the p-adic exponential ring
  • 4
  • Highly Influenced
  • PDF
Model theory of holomorphic functions
Expansions of the Real Field with Power Functions
  • 91
  • PDF
Geometry, calculus and Zil'ber's conjecture
  • 9
Definable functions in tame expansions of algebraically closed valued fields
  • 2
  • PDF
An effective version of Wilkie's theorem of the complement and some effective o-minimality results
  • 15
  • PDF
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 26 REFERENCES
On the Elementary Theory of Restricted Elementary Functions
  • L. Dries
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 1988
  • 49
DEFINABLE SETS IN ORDERED STRUCTURES. I
  • 293
  • PDF
A Decision Method For Elementary Algebra And Geometry
  • 1,560
Definable sets in ordered structures
  • 208
  • PDF
adic and real subanalytic sets
  • Ann. of Math
  • 1988
An Introduction to Linear Algebra
  • 267
  • Highly Influential
Introduction to Linear Algebra
  • 1,523
...
1
2
3
...