451 research outputs found
Existentially closed fields with G-derivations
We prove that the theories of fields with Hasse-Schmidt derivations
corresponding to actions of formal groups admit model companions. We also give
geometric axiomatizations of these model companions.Comment: In version 2: new proof of (the current) Proposition 3.3
On Kirchberg's Embedding Problem
Kirchberg's Embedding Problem (KEP) asks whether every separable C
algebra embeds into an ultrapower of the Cuntz algebra . In this
paper, we use model theory to show that this conjecture is equivalent to a
local approximate nuclearity condition that we call the existence of good
nuclear witnesses. In order to prove this result, we study general properties
of existentially closed C algebras. Along the way, we establish a
connection between existentially closed C algebras, the weak expectation
property of Lance, and the local lifting property of Kirchberg. The paper
concludes with a discussion of the model theory of . Several
results in this last section are proven using some technical results concerning
tubular embeddings, a notion first introduced by Jung for studying embeddings
of tracial von Neumann algebras into the ultrapower of the hyperfinite II
factor.Comment: 42 pages; final version to appear in the Journal of Functional
Analysi
Some applications of the ultrapower theorem to the theory of compacta
The ultrapower theorem of Keisler-Shelah allows such model-theoretic notions
as elementary equivalence, elementary embedding and existential embedding to be
couched in the language of categories (limits, morphism diagrams). This in turn
allows analogs of these (and related) notions to be transported into unusual
settings, chiefly those of Banach spaces and of compacta. Our interest here is
the enrichment of the theory of compacta, especially the theory of continua,
brought about by the immigration of model-theoretic ideas and techniques
Some Applications of the Ultrapower Theorem to the Theory of Compacta
The ultrapower theorem of Keisler and Shelah allows such model-theoretic notions as elementary equivalence, elementary embedding and existential embedding to be couched in the language of categories (limits, morphism diagrams). This in turn allows analogs of these (and related) notions to be transported into unusual settings, chiefly those of Banach spaces and of compacta. Our interest here is the enrichment of the theory of compacta, especially the theory of continua, brought about by the importation of model-theoretic ideas and techniques
The Freiheitssatz for generic Poisson algebras
We prove the Freiheitssatz for the variety of generic Poisson algebras
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