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Algebra Logika, 2003, Volume 42, Number 2, Pages 194–210 (Mi al25)  

This article is cited in 17 scientific papers (total in 17 papers)

$E^*$-Stable Theories

E. A. Palyutin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: S. Shelah proved that stability of a theory is equivalent to definability of every complete type of that theory. T. Mustafin introduced the concept of being $T^*$-stable, generalizing the notion of being stable. However, $T^*$-stability does not necessitate definability of types. The key result of the present article is proving the definability of types for $E^*$-stable theories. This concept differs from that of being $T^*$-stable by adding the condition of being continuous. As a consequence we arrive at the definability of types over any $P$-sets in $P$-stable theories, which previously was established by T. Nurmagambetov and B. Poizat for types over $P$-models.

Keywords: $E^*$-stable theory, definability of types.

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English version:
Algebra and Logic, 2003, 42:2, 112–120

Bibliographic databases:

UDC: 510.67:512.57
Received: 04.04.2001

Citation: E. A. Palyutin, “$E^*$-Stable Theories”, Algebra Logika, 42:2 (2003), 194–210; Algebra and Logic, 42:2 (2003), 112–120

Citation in format AMSBIB
\by E.~A.~Palyutin
\paper $E^*$-Stable Theories
\jour Algebra Logika
\yr 2003
\vol 42
\issue 2
\pages 194--210
\jour Algebra and Logic
\yr 2003
\vol 42
\issue 2
\pages 112--120

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    This publication is cited in the following articles:
    1. E. A. Palyutin, “Elementary Pairs of Primitive Normal Theories”, Algebra and Logic, 43:3 (2004), 179–189  mathnet  crossref  mathscinet  zmath
    2. E. A. Palyutin, “Stably Definable Classes of Theories”, Algebra and Logic, 44:5 (2005), 326–335  mathnet  crossref  mathscinet  zmath
    3. M. A. Rusaleev, “Characterization of $(p,1)$-stable theories”, Algebra and Logic, 46:3 (2007), 188–194  mathnet  crossref  mathscinet  zmath  isi
    4. A. R. Yeshkeyev, “On Jonsson stability and some of its generalizations”, J. Math. Sci., 166:5 (2010), 646–654  mathnet  crossref  mathscinet
    5. M. A. Rusaleev, “Generalized stability of torsion-free Abelian groups”, Algebra and Logic, 50:2 (2011), 161–170  mathnet  crossref  mathscinet  zmath  isi
    6. B. S. Baizhanov, V. V. Verbovskii, “$o$-stable theories”, Algebra and Logic, 50:3 (2011), 211–225  mathnet  crossref  mathscinet  zmath  isi
    7. E. A. Palyutin, “$P$-stable Abelian groups”, Algebra and Logic, 52:5 (2013), 404–421  mathnet  crossref  mathscinet  isi
    8. E. A. Palyutin, “$P$-spectra of Abelian groups”, Algebra and Logic, 53:2 (2014), 140–165  mathnet  crossref  mathscinet  isi
    9. E. A. Palyutin, “Theories of $P$-expansions of Abelian groups”, Algebra and Logic, 54:2 (2015), 183–187  mathnet  crossref  crossref  mathscinet  isi
    10. E. A. Palyutin, “Totally $P$-stable Abelian groups”, Algebra and Logic, 54:4 (2015), 296–315  mathnet  crossref  crossref  mathscinet  isi
    11. A. A. Stepanova, D. O. Ptakhov, “$P$-stable polygons”, Algebra and Logic, 56:4 (2017), 324–336  mathnet  crossref  crossref  isi
    12. Yeshkeyev A.R., “About Central Types and the Cosemanticness of the Delta-Pm Fragment of the Jonsson Set”, Bull. Karaganda Univ-Math., 87:3 (2017), 51–58  isi
    13. D. O. Ptakhov, “Polygons with a (P, 1)-stable theory”, Algebra and Logic, 56:6 (2018), 473–478  mathnet  crossref  crossref  isi
    14. Yeshkeyev A.R. Kassymetova M.T. Ulbrikht O.I., “Criterion For the Cosemanticness of the Abelian Groups in the Enriched Signature”, Bull. Karaganda Univ-Math., 89:1 (2018), 49–60  mathscinet  isi
    15. Yeshkeyev A.R., Omarova M.T., “Central Types of Convex Fragments of the Perfect Jonsson Theory”, Bull. Karaganda Univ-Math., 93:1 (2019), 95–101  crossref  isi
    16. A. A. Stepanova, A. I. Krasitskaya, “$P$-stabilnost nekotorykh klassov $S$-poligonov”, Sib. matem. zhurn., 62:2 (2021), 441–449  mathnet  crossref
    17. A. R. Yeshkeyev, M. T. Kassymetova, O. I. Ulbrikht, “Independence and simplicity in Jonsson theories with abstract geometry”, Sib. elektron. matem. izv., 18:1 (2021), 433–455  mathnet  crossref
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