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The limit theory of generic polynomials

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Published online by Cambridge University Press:  31 March 2017

Matthias Baaz
Affiliation:
Technische Universität Wien, Austria
Sy-David Friedman
Affiliation:
Universität Wien, Austria
Jan Krajíček
Affiliation:
Academy of Sciences of the Czech Republic, Prague
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Logic Colloquium '01 , pp. 242 - 254
Publisher: Cambridge University Press
Print publication year: 2005

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References

[1] L., Blum, F., Cucker, M., Shub, and S., Smale, Complexity and real computation, Springer- Verlag, 1998.
[2] O., Chapuis, E., Hrushovski, P., Koiran, and B., Poizat, La limite des thèories de courbes gènèriques, The Journal of Symbolic Logic, vol. 67 (2002), pp. 24–34.Google Scholar
[3] P., Koiran, On defining irreducibility, Comptes Rendus de l'Acadèmie des Sciences, vol. 330 (2000), pp. 529–532.Google Scholar
[4] P., Koiran, The theory of Liouville functions, The Journal of Symbolic Logic, vol. 68 (2003), no. 2, pp. 353–365.Google Scholar
[5] P., Koiran and N., Portier, Back-and-forth systems for generic curves and a decision algorithm for the limit theory, Annals of Pure and Applied Logic, vol. 111 (2001), pp. 257–275.Google Scholar
[6] P., Koiran, N., Portier, and G., Villard, A rank theorem for Vandermonde matrices, Linear Algebra and Its Applications, vol. 378 (2004), pp. 99–107.Google Scholar
[7] D., Perrin, Gèomètrie algèbrique: une introduction, Interèditions / CNRS Editions, 1995.
[8] B., Poizat, Amalgames de Hrushovski: une tentative de classification, Tits buildings and the model theory of groups (Würzburg, 2000), London Mathematical Society Lecture Note Series, 291, Cambridge University Press, Cambridge, 2002.
[9] A. J., Wilkie, On defining, The Journal of Symbolic Logic, vol. 59 (1994), no. 1, p. 344.
[10] A. J., Wilkie, O-minimality, Documenta Mathematica, vol. I (1998), pp. 633–636, http:// www.mathematik.uni-bielefeld.de/documenta, Extra Volume ICM 1998.Google Scholar
[11] A. J., Wilkie, Liouville functions, Logic colloquium 2000 (R., Cori et al., editors), Lecture Notes in Logic, vol. 19, AK Peters, to appear.
[12] B., Zilber, A theory of a generic function with derivations, Logic and algebra (Yi, Zhang, editor), Contemporary Mathematics, vol. 302, American Mathematical Society, 2002, pp. 85–100.

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