Transactions of the American Mathematical Society

Author(s): Rahim Moosa
Journal: Trans. Amer. Math. Soc. 356 (2004), 1781-1797.
MSC (2000): Primary 03C60; Secondary 32J99
Posted: January 6, 2004
Retrieve article in: PDF

Abstract: We study elementary extensions of compact complex spaces and deduce that every complete type of dimension

is internal to projective space. This amounts to a nonstandard version of the Riemann Existence Theorem, and answers a question posed by Anand Pillay.

1.: F. Campana.
Coréduction algébrique d'un espace analytique faiblement Kählérien compact.
Inventiones Mathematicae, (63):187-223, 1981. MR 84e:32028
2.: F. Campana and T. Peternell.
Cycle spaces.
In Grauert et al. [6], pages 319-349. MR 96k:32001
3.: G. Fischer.
Complex Analytic Geometry.
Springer-Verlag, Berlin, 1976. MR 55:3291
4.: A. Fujiki.
On a holomorphic fibre bundle with meromorphic structure.
Publications of the Research Institute for Mathemtaical Sciences, 19(1):117-134, 1983. MR 84m:32038
5.: A. Fujiki.
On the structure of compact complex manifolds in $\mathcal{C}$ .
In Algebraic Varieties and Analytic Varieties, volume 1 of Advanced Studies in Pure Mathematics, pages 231-302. North-Holland, Amsterdam, 1983. MR 85g:32045b
6.: H. Grauert, T. Peternell, and R. Remmert, editors.
Several Complex Variables VII, volume 74 of Encyclopedia of Mathematical Sciences.
Springer-Verlag, Berlin, 1994. MR 96k:32001
7.: R. Gunning and H. Rossi.
Analytic functions of several complex variables.
Prentice-Hall, Edgewood Cliffs, 1965. MR 31:4927
8.: W. Hodges.
Model Theory.
Cambridge University Press, Cambridge, 1993. MR 94e:03002
9.: R. Moosa.
The model theory of compact complex spaces.
To appear in the Proceedings of the Logic Colloquium '01 (Vienna).
10.: R. Moosa.
On saturation and the model theory of compact Kähler manifolds.
Preprint.
11.: R. Moosa.
Contributions to the model theory of fields and compact complex spaces.
PhD thesis, University of Illinois, Urbana-Champaign, 2001.
12.: T. Peternell and R. Remmert.
Differential calculus, holomorphic maps and linear structures on complex spaces.
In Grauert et al. [6], pages 97-144. MR 96k:32001
13.: A. Pillay.
Some model theory of compact complex spaces.
In Workshop on Hilbert's tenth problem: relations with arithmetic and algebraic geometry, volume 270 of Contemporary Mathematics, Amer. Math. Soc., Providence, RI, 2000, pp. 323-338. MR 2001m:03076
14.: B. Poizat.
Groupes stables.
Nur al-Mantiq wal-Ma'rifah, Villeurbanne, 1987. MR 89b:03056
15.: R. Remmert.
Local theory of complex spaces.
In Grauert et al. [6], pages 10-96. MR 96k:32001
16.: K. Ueno.
Classification Theory of Algebraic Varieties and Compact Complex Spaces, volume 439 of Lecture Notes in Mathematics.
Springer-Verlag, Berlin, 1975. MR 58:22062
17.: B. Zilber.
Model theory and algebraic geometry.
In Proceedings of the 10th Easter Conference on Model Theory, Berlin, 1993.

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 03C60, 32J99

Rahim Moosa
Affiliation: The Fields Institute, 222 College Street, Toronto, Ontario, Canada M5T 3J1
Address at time of publication: Massachusetts Institute of Technology, Department of Mathematics, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307
Email: moosa@math.mit.edu

DOI: 10.1090/S0002-9947-04-03559-7
PII: S 0002-9947(04)03559-7
Received by editor(s): July 17, 2002
Posted: January 6, 2004
Additional Notes: This work was supported by the Natural Science and Engineering Research Council of Canada
Copyright of article: Copyright 2004, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS