Geodesic
Local Stability and Saturation in Spaces of Orderings
Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 454-477

Voir la notice de l'article provenant de la source Cambridge University Press

If k is a f.r. (= formally real) field which is partially ordered with positive cone, P, XP denotes the space of total orders T of k with P ⊂ T. Suppose you have a subset A ⊂ XP and an element T ∈ XP , T ∉ A. Then the main question investigated in this paper is the following: How can T be separated from A by using elements of k? To be more specific, this is split up into two different questions. Question 1. Suppose A is closed. Then there is an n ∈ N and elements a 1, ..., an ∈ k such that the basic open set H = H(a 1, ..., an ) is a neighborhood of T and has empty intersection with A. Now, if T is given, what is the least n ∊ N (if it exists) such that T has a neighborhood basis consisting of basic open sets of the form H(a 1, ..., an )? 
Schwartz, Niels. Local Stability and Saturation in Spaces of Orderings. Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 454-477. doi: 10.4153/CJM-1983-025-x
@article{10_4153_CJM_1983_025_x,
     author = {Schwartz, Niels},
     title = {Local {Stability} and {Saturation} in {Spaces} of {Orderings}},
     journal = {Canadian journal of mathematics},
     pages = {454--477},
     year = {1983},
     volume = {35},
     number = {3},
     doi = {10.4153/CJM-1983-025-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-025-x/}
}
TY  - JOUR
AU  - Schwartz, Niels
TI  - Local Stability and Saturation in Spaces of Orderings
JO  - Canadian journal of mathematics
PY  - 1983
SP  - 454
EP  - 477
VL  - 35
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-025-x/
DO  - 10.4153/CJM-1983-025-x
ID  - 10_4153_CJM_1983_025_x
ER  - 
%0 Journal Article
%A Schwartz, Niels
%T Local Stability and Saturation in Spaces of Orderings
%J Canadian journal of mathematics
%D 1983
%P 454-477
%V 35
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-025-x/
%R 10.4153/CJM-1983-025-x
%F 10_4153_CJM_1983_025_x

[1] 1. Becker, E. and Bröcker, L., On the description of the reduced Witt ring, J. Alg. 52 (1978), 328–346. Google Scholar

[2] 2. Becker, E. and Köing, E., Reduzierte quadratische Formen, Abh. Math. Sem. Univ. Hamb. 46 (1977), 143–177. Google Scholar

[3] 3. Bröcker, L., Zur Theorie der quadratischen Formen über formal reellen Körpern, Math. Ann. 270 (1974), 233–256. Google Scholar

[4] 4. Bröcker, L., Characterization of fans and hereditarily pythagorean fields, Math. Z. 151 (1976), 149–163. Google Scholar

[5] 5. Bröcker, L., Über die Anzahl der Anordnungen eines kommutativen Körpers, Arch. Math. 29 (1977), 458–464. Google Scholar

[6] 6. Coste, M. and Coste-Roy, M.-F., La topologie du spectre reel, Preprint. Google Scholar

[7] 7. Craven, T., Stability in Witt rings, Transactions AMS 225 (1977), 227–242. Google Scholar

[8] 8. Dubois, D. W., Infinite primes and ordered fields, Dissertationes Math. 69 (1970). Google Scholar

[9] 9. Elman, R. and Lam, T. Y., Quadratic forms over formally real fields and pythagorean fields, Amer. J. M. 94 (1972), 1155–1194. Google Scholar

[10] 10. Elman, R., Lam, T. Y. and Wadsworth, A., Pfister ideals in Witt-rings, Math. Ann. 245 (1979), 219–245. Google Scholar

[11] 11. Kleinstein, J., Abstract Witt rings, Thesis. Google Scholar

[12] 12. Kleinstein, J., Abstract Witt rings, In: Conference on quadratic forms – 1976, Kingston, Ontario (1977). Google Scholar

[13] 13. Kleinstein, J. and Rosenberg, A., Signatures and semisignatures of abstract Witt rings and Witt rings of semilocal rings, Can. J. Math. 30 (1978), 872–895. Google Scholar

[14] 14. Knebusch, M., Rosenberg, A. and Ware, R., Signatures on semilocal rings, J. Alg. 26 (1973), 208–250. Google Scholar

[15] 15. Lam, T. Y., The algebraic theory of quadratic forms (Benjamin, Reading, Mass., 1973). Google Scholar

[16] 16. Marshall, M., Classification of finite spaces of orderings, Can. J. Math. 31 (1979), 320–330. Google Scholar

[17] 17. Marshall, M., The Witt ring of a space of orderings, Transactions AMS 258 (1980), 505–521. Google Scholar

[18] 18. Marshall, M., Spaces of orderings IV, Preprint. Google Scholar | DOI

[19] 19. Prestel, A., Lectures on formally real fields, IMPA, Rio de Janeiro (1975). Google Scholar

[20] 20. Schülting, H.-W., Über reelle Stellen eines Körpers und ihren Holomorphiering, Dissertation. Dortmund (1979). Google Scholar

Cité par Sources :