On the number of generic models
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Vincent Lee, Mark Nadel (1975)
Fundamenta Mathematicae
Stanisław Kasjan (2002)
Fundamenta Mathematicae
Associative algebras of fixed dimension over algebraically closed fields of fixed characteristic are considered. It is proved that the class of algebras of tame representation type is axiomatizable. Moreover, finite axiomatizability of this class is equivalent to the conjecture that the algebras of tame representation type form a Zariski-open subset in the variety of algebras.
Morozov, A.S. (2003)
Sibirskij Matematicheskij Zhurnal
N. A. Shanin (1977)
Zbornik Radova
Morozov, A.S. (2004)
Sibirskij Matematicheskij Zhurnal
J.L. Bell (1972)
Archiv für mathematische Logik und Grundlagenforschung
Stanley Burris, Errol Jeffers (1978)
Colloquium Mathematicae
Shlomo Vinner (1975)
Archiv für mathematische Logik und Grundlagenforschung
Stanisław Kasjan, Grzegorz Pastuszak (2011)
Colloquium Mathematicae
Let k be a field of characteristic different from 2. We consider two important tame non-polynomial growth algebras: the incidence k-algebra of the garland 𝒢₃ of length 3 and the incidence k-algebra of the enlargement of the Nazarova-Zavadskij poset 𝒩 𝓩 by a greatest element. We show that if Λ is one of these algebras, then there exists a special family of pointed Λ-modules, called an independent pair of dense chains of pointed modules. Hence, by a result of Ziegler, Λ admits a super-decomposable...
Thomas Blossier, Amador Martin-Pizarro, Frank O. Wagner (2012)
Fundamenta Mathematicae
We introduce a generalisation of CM-triviality relative to a fixed invariant collection of partial types, in analogy to the Canonical Base Property defined by Pillay, Ziegler and Chatzidakis which generalises one-basedness. We show that, under this condition, a stable field is internal to the family, and a group of finite Lascar rank has a normal nilpotent subgroup such that the quotient is almost internal to the family.
Khisamiev, A.N. (2006)
Sibirskij Matematicheskij Zhurnal
Angus Macintyre (1971)
Fundamenta Mathematicae
Angus Macintyre (1971)
Fundamenta Mathematicae
Y. Suzuki (1970)
Fundamenta Mathematicae
Bovykin, Andrey (2004)
Lobachevskii Journal of Mathematics
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