Geodesic
Symmetry of Sections in Fields of Formal Power Series and a Non-Standard Real Line
Algebra i logika, Tome 42 (2003) no. 1, pp. 26-36.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $R[[G,\beta]]$ be a field of formal power series with real coefficients, whose supports are well ordered subsets of an Abelian group $G$ of cardinality strictly less than $\beta$. For $R[[G,\beta]]$, we give criteria of a section being symmetric and of a symmetric section being Dedekind. It is proved that an $\alpha^+$-saturated non-standard real line $^{*}R$ is isomorphic to some field of the form $R[[G,\alpha^+]]$. For $^{*}R$, some consequences are inferred regarding symmetric sections, and the cofinality of “banks” of the sections. 
@article{AL_2003_42_1_a1,
     author = {N. Yu. Galanova},
     title = {Symmetry of {Sections} in {Fields} of {Formal} {Power} {Series} and a {Non-Standard} {Real} {Line}},
     journal = {Algebra i logika},
     pages = {26--36},
     publisher = {mathdoc},
     volume = {42},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2003_42_1_a1/}
}
TY  - JOUR
AU  - N. Yu. Galanova
TI  - Symmetry of Sections in Fields of Formal Power Series and a Non-Standard Real Line
JO  - Algebra i logika
PY  - 2003
SP  - 26
EP  - 36
VL  - 42
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2003_42_1_a1/
LA  - ru
ID  - AL_2003_42_1_a1
ER  - 
%0 Journal Article
%A N. Yu. Galanova
%T Symmetry of Sections in Fields of Formal Power Series and a Non-Standard Real Line
%J Algebra i logika
%D 2003
%P 26-36
%V 42
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2003_42_1_a1/
%G ru
%F AL_2003_42_1_a1
N. Yu. Galanova. Symmetry of Sections in Fields of Formal Power Series and a Non-Standard Real Line. Algebra i logika, Tome 42 (2003) no. 1, pp. 26-36. http://geodesic.mathdoc.fr/item/AL_2003_42_1_a1/

[1] L. Fuks, Chastichno uporyadochennye algebraicheskie sistemy, Mir, M., 1965 | MR

[2] H. J. Dales, H. Woodin, Super real fields, Clarendon Press, Oxford, 1996 | MR | Zbl

[3] G. G. Pestov, Stroenie uporyadochennykh polei, izd-vo TGU, Tomsk, 1980 | MR

[4] G. G. Pestov, “Simmetriya sechenii v uporyadochennom pole”, Izbr. dokl. mezhd. konf. “Vsesibirskie chteniya po matematike i mekhanike”, 1, izd-vo TGU, Tomsk, 1997, 198–203

[5] G. G. Pestov, “K teorii sechenii v uporyadochennykh polyakh”, Sib. matem. zh., 42:6 (2001), 1350–1360 | MR | Zbl

[6] E. Artin, O. Schreier, “Algebraische Konstruktion Reeller Körper”, Abh. Math. Semin. Univ. Hamb., 5 (1925), 85–99 | DOI

[7] Spravochnaya kniga po mat. logike, ch. 1: Teoriya modelei, Nauka, M., 1982 | MR

[8] B. Delay, “Coupures propres dans ${}^*R$”, Ann. Math. Blaise Pascal, 4:1 (1997), 19–25 | MR | Zbl

[9] N. I. Galanova, “Konfinalnost i simmetrichnost sechenii v uporyadochennykh polyakh”, Issledovaniya po matematicheskomu analizu i algebre, izd-vo TGU, Tomsk, 1998, 138–143