Convexity relations and generalizations of o-minimality
Matematičeskie trudy, Tome 21 (2018) no. 1, pp. 35-54.

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

We suggest generalizations of the notion of o-minimality. Namely, we introduce and study the notions of multi-$R$-minimality and right o-minimality (with modifications).
@article{MT_2018_21_1_a2,
     author = {K. Zh. Kudaǐbergenov},
     title = {Convexity relations and generalizations of o-minimality},
     journal = {Matemati\v{c}eskie trudy},
     pages = {35--54},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2018_21_1_a2/}
}
TY  - JOUR
AU  - K. Zh. Kudaǐbergenov
TI  - Convexity relations and generalizations of o-minimality
JO  - Matematičeskie trudy
PY  - 2018
SP  - 35
EP  - 54
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2018_21_1_a2/
LA  - ru
ID  - MT_2018_21_1_a2
ER  - 
%0 Journal Article
%A K. Zh. Kudaǐbergenov
%T Convexity relations and generalizations of o-minimality
%J Matematičeskie trudy
%D 2018
%P 35-54
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2018_21_1_a2/
%G ru
%F MT_2018_21_1_a2
K. Zh. Kudaǐbergenov. Convexity relations and generalizations of o-minimality. Matematičeskie trudy, Tome 21 (2018) no. 1, pp. 35-54. http://geodesic.mathdoc.fr/item/MT_2018_21_1_a2/

[1] Kudaibergenov K. Zh., “Malye rasshireniya modelei $\mathrm{o}$-minimalnykh teorii i absolyutnaya odnorodnost”, Matem. tr., 10:1 (2007), 154–163 | MR | Zbl

[2] Kudaibergenov K. Zh., “Slabo kvazi-$\mathrm{o}$-minimalnye modeli”, Matem. tr., 13:1 (2010), 156–168 | MR

[3] Kudaibergenov K. Zh., “O svoistve nezavisimosti teorii pervogo poryadka i nerazlichimykh posledovatelnostyakh”, Matem. tr., 14:1 (2011), 126–140 | MR | Zbl

[4] Kudaibergenov K. Zh., “Obobschenie $$\mathrm{o}$$-minimalnosti na chastichnye poryadki”, Matem. tr., 15:1 (2012), 86–108 | Zbl

[5] Melnikov O. V., Remeslennikov V. N., Romankov V. A., Skornyakov L. A., Shestakov I. P., Obschaya algebra, v. 1, Nauka, M., 1990 | MR

[6] Belegradek O., Peterzil Y., Wagner F., “Quasi-$\mathrm{o}$-minimal structures”, J. Symbolic Logic, 65:3 (2000), 1115–1132 | DOI | MR | Zbl

[7] Bhattacharjee M., Macpherson D., Möller R. G., Neumann P. M., Notes on Infinite Permutation Groups, Lecture Notes in Math., 1698, Springer, Berlin, 1998 | DOI | MR | Zbl

[8] Dickmann M. A., “Elimination of quantifiers for ordered valuation rings”, Proc. of the 3rd Easter Conf. on Model Theory (Gross Koris, 1985), Humboldt Univ., Berlin, 1985, 64–88 | MR | Zbl

[9] van den Dries L., “Remarks on Tarski's problem concerning $(R,+,\cdot,{\rm{exp}})$”, Logic Colloquium'82 (Florence, 1982), Stud. Logic Found. Math., 112, North-Holland, Amsterdam, 1984, 97–121 | DOI | MR

[10] Hodges W., Model Theory, Encyclopedia of Mathematics and Its Applications, 42, Cambridge Univ. Press, Cambridge, 1993 | MR | Zbl

[11] Knight J., Pillay A., Steinhorn C., “Definable sets in ordered structures. II”, Trans. Amer. Math. Soc., 295:2 (1986), 593–605 | DOI | MR | Zbl

[12] Kunen K., Combinatorics, Handbook of Mathematical Logic, North-Holland Publishing Co., Amsterdam, 1977 | MR

[13] Macpherson D., Steinhorn C., “On variants of $\mathrm{o}$-minimality”, Ann. Pure Appl. Logic, 79:2 (1996), 165–209 | DOI | MR | Zbl

[14] Macpherson D., Marker D., Steinhorn C., “Weakly $\mathrm{o}$-minimal structures and real closed fields”, Trans. Amer. Math. Soc., 352:12 (2000), 5435–5483 | DOI | MR | Zbl

[15] Marker D., “Omitting types in $\mathcal O$-minimal theories”, J. Symbolic Logic, 51:1 (1986), 63–74 | DOI | MR | Zbl

[16] Newelski L., Wencel R., “Definable sets in Boolean-ordered $\mathrm{o}$-minimal structures. I”, J. Symbolic Logic, 66:4 (2001), 1821–1836 | DOI | MR | Zbl

[17] Pillay A. Steinhorn C., “Definable sets in ordered structures. I”, Trans. Amer. Math. Soc., 295:2 (1986), 565–592 | DOI | MR | Zbl

[18] Poizat B., “Théories instables”, J. Symbolic Logic, 46 (1981), 513–522 | DOI | MR | Zbl

[19] Shelah S., Classification Theory and the Number of Nonisomorphic Models, Studies in Logic and the Foundations of Mathematics, 92, North-Holland Publishing Co., Amsterdam–New York, 1978 | MR

[20] Toffalori C., “Lattice ordered $\mathrm{o}$-minimal structures”, Notre Dame J. Formal Logic, 39:4 (1998), 447–463 | DOI | MR | Zbl