Remark on o-stable pure ordered groups
DOI:
https://doi.org/10.70474/5c1hpw60Keywords:
ordered group, NIP theory, o-minimal theory, o-stable theory, o-superstable theoryAbstract
In this article, we describe pure ordered groups, whose elementary theory is o-stable or o-superstable.
The notion of o-stability is a natural combination of stability and o-minimality, namely, an ordered structure is called o-stable if any of its cuts are consistent with a few complete one-types.
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Adler H. Strong theories, burden, and weight. Preprint from 2007. DOI: https://doi.org/10.1126/stke.3902007tw202
Baizhanov B., and Verbovskii V. O-stable theories, Algebra and Logic, 50:3 (2011), 211–225. DOI: https://doi.org/10.1007/s10469-011-9136-7
Baldwin J. and Saxl J. Logical stability in group theory, J. Austral. Math. Soc. Ser. A, 21:3 (1976), 267–276. DOI: https://doi.org/10.1017/S1446788700018553
Gurevich Y., Schmitt P.H., The theory of ordered abelian groups does not have the independence property, Trans. Amer. Math. Soc. 284:1 (1984), 171–182. DOI: https://doi.org/10.1090/S0002-9947-1984-0742419-0
Jahnke F., Simon P., and Walsberg E. DP-minimal valued fields, Journal of Symbolic Logic 82 (2017), 151–165. DOI: https://doi.org/10.1017/jsl.2016.15
Poizat B. Groupes Stables, Nur al-Mantiq wal-M´arifah, 2. Lyon: Bruno Poizat, 1987.
Simon P. On dp-minimal ordered structures. J. Symbolic Logic 76:2 (2011), 448–460. DOI: https://doi.org/10.2178/jsl/1305810758
Verbovskiy V. V. Ob eliminacii kvantorov dlya (R, <, +, H) s vydelennoy plotnoy podgruppoy, Matematicheskiy zhurnal, 6:2 (2006), 56–59.
Verbovskiy V. V. Dp-minimalnye i uporyadochenno stabilnye uporyadochennye structure, Matematicheskiy zhurnal, 10:2 (2010), 35–38.
Verbovskiy V. V. O-stable ordered groups, Siberian Advances in Mathematics, 22:1 (2012), 50–74 DOI: https://doi.org/10.3103/S105513441201004X
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