Geodesic
Binarity and $\aleph_0$-categoricity for variants of o-minimality
Eurasian mathematical journal, Tome 2 (2011) no. 2, pp. 89-107.

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

The present work is a survey paper devoted to studying two variants of o-minimality: weak o-minimality and weak circular minimality (mostly in the $\aleph_0$-categorical case). 
@article{EMJ_2011_2_2_a4,
     author = {B. Sh. Kulpeshov},
     title = {Binarity and $\aleph_0$-categoricity for variants of o-minimality},
     journal = {Eurasian mathematical journal},
     pages = {89--107},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a4/}
}
TY  - JOUR
AU  - B. Sh. Kulpeshov
TI  - Binarity and $\aleph_0$-categoricity for variants of o-minimality
JO  - Eurasian mathematical journal
PY  - 2011
SP  - 89
EP  - 107
VL  - 2
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a4/
LA  - en
ID  - EMJ_2011_2_2_a4
ER  - 
%0 Journal Article
%A B. Sh. Kulpeshov
%T Binarity and $\aleph_0$-categoricity for variants of o-minimality
%J Eurasian mathematical journal
%D 2011
%P 89-107
%V 2
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a4/
%G en
%F EMJ_2011_2_2_a4
B. Sh. Kulpeshov. Binarity and $\aleph_0$-categoricity for variants of o-minimality. Eurasian mathematical journal, Tome 2 (2011) no. 2, pp. 89-107. http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a4/

[1] S. Adeleke, H. D. Macpherson, “Classification of infinite primitive Jordan permutation groups”, Proc. London Math. Soc. Ser. 3, 72 (1995), 63–123 | DOI | MR

[2] S. Adeleke, P. M. Neumann, “Primitive permutation groups with primitive Jordan sets”, J. London Math. Soc. Ser. 2, 53 (1996), 209–229 | DOI | MR | Zbl

[3] R. D. Arefiev, “On monotonicity property for weakly o-minimal models”, Algebra and Model Theory, eds. A. G. Pinus, K. N. Ponomaryov, Novosibirsk, 1997, 8–15

[4] B. S. Baizhanov, “Orthogonality of one-types in weakly o-minimal theories”, Algebra and Model Theory, v. II, eds. A. G. Pinus, K. N. Ponomaryov, Novosibirsk State Technical University, 1999, 3–28 | MR

[5] B. S. Baizhanov, “Expansion of a model of a weakly o-minimal theory by a family of unary predicates”, The Journal of Symbolic Logic, 66 (2001), 1382–1414 | DOI | MR | Zbl

[6] M. Bhattacharjee, H. D. Macpherson, R. G. Möller, P. M. Neumann, Notes on Infinite Permutation Groups, Lecture Notes in Mathematics, 1698, Springer-Verlag, Berlin–Heidelberg, 1998 | MR | Zbl

[7] P. J. Cameron, “Orbits of permutation groups on unordered sets, II”, J. London Math. Soc., 2 (1981), 249–264 | DOI | MR | Zbl

[8] M. Dickmann, “Elimination of quantifiers for ordered valuation rings”, J. Symb. Logic, 52 (1987), 116–128 | DOI | MR | Zbl

[9] M. Droste, M. Giraudet, H. D. Macpherson, N. Sauer, “Set-homogeneous graphs”, J. Comb. Theory, Series B, 62:1 (1994), 63–95 | DOI | MR | Zbl

[10] D. Haskell, H. D. Macpherson, “A version of o-minimality for the $p$-adics”, J. Symb. Logic, 62 (1997), 1075–1092 | DOI | MR | Zbl

[11] B. Herwig, H. D. Macpherson, G. Martin, A. Nurtazin, J. K. Truss, “On $\aleph_0$-categorical weakly o-minimal structures”, Ann. Pure Appl. Logic, 101 (2000), 65–93 | DOI | MR | Zbl

[12] B. Sh. Kulpeshov, “Weakly o-minimal structures and some of their properties”, J. Symb. Logic, 63 (1998), 1511–1528 | DOI | MR | Zbl

[13] B. Sh. Kulpeshov, “Criterion for binarity of $\aleph_0$-categorical weakly o-minimal theories”, Annals of Pure and Applied Logic, 145 (2007), 354–367 | DOI | MR | Zbl

[14] B. Sh. Kulpeshov, “The property of being binary for $\aleph_0$-caterorical weakly o-minimal theories”, Algebra and Logic, 44:4 (2005), 256–263 | DOI | MR | Zbl

[15] B. Sh. Kulpeshov, H. D. Macpherson, “Minimality conditions on circularly ordered structures”, Mathematical Logic Quarterly, 51 (2005), 377–399 | DOI | MR | Zbl

[16] B. Sh. Kulpeshov, “Definable functions in $\aleph_0$-categorical weakly circularly minimal structures”, Siberian Mathematical Journal, 50:2 (2009), 282–301 | DOI | MR | Zbl

[17] B. Sh. Kulpeshov, “On $\aleph_0$-categorical weakly circularly minimal structures”, Mathematical Logic Quarterly, 52 (2006), 555–574 | DOI | MR | Zbl

[18] A. H. Lachlan, “Countable homogeneous tournaments”, Trans. Amer. Math. Soc., 284 (1984), 431–461 | DOI | MR | Zbl

[19] H. D. Macpherson, C. Steinhorn, “On variants of o-minimality”, Ann. Pure Appl. Logic, 79 (1996), 165–209 | DOI | MR | Zbl

[20] H. D. Macpherson, D. Marker, C. Steinhorn, “Weakly o-minimal structures and real closed fields”, Trans. Amer. Math. Soc., 352 (2000), 5435–5483 | DOI | MR | Zbl

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

[22] C. Toffalori, “Lattice ordered o-minimal structures”, Notre Dame J. Formal Logic, 39 (1998), 447–463 | DOI | MR | Zbl

[23] V. V. Verbovskiy, “Non uniformly weakly o-minimal group”, Algebra and Model Theory, Collection of papers, v. 3, eds. A. G. Pinus, K. N. Ponomaryov, Novosibirsk, 2001, 136–145 | MR | Zbl

[24] R. Wencel, “Small theories of Boolean ordered o-minimal structures”, J. Symb. Logic, 67 (2002), 1385–1390 | DOI | MR | Zbl