SOME DEFINABLE GALOIS THEORY AND EXAMPLES
نویسندگان
چکیده
منابع مشابه
Some Definable Galois Theory and Examples
We make explicit certain results around the Galois correspondence in the context of definable automorphism groups, and point out the relation to some recent papers dealing with the Galois theory of algebraic differential equations when the constants are not “closed” in suitable senses. We also improve the definitions and results from [15] on generalized strongly normal extensions, using this to...
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1. Examples Example 1.1. The field extension Q(√ 2, √ 3)/Q is Galois of degree 4, so its Galois group has order 4. The elements of the Galois group are determined by their values on √ 2 and √ 3. The Q-conjugates of √ 2 and √ 3 are ± √ 2 and ± √ 3, so we get at most four possible automorphisms in the Galois group. See Table 1. Since the Galois group has order 4, these 4 possible assignments of v...
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It is well-known that dimX ≤ n if and only if every map of a closed subspace of X into the n-dimensional sphere Sn can be extended over X. It is also well-known that for the cohomological dimension dimGX of X with respect to an abelian coefficient group G, dimGX ≤ n if and only if every map of a closed subspace of X into the Eilenberg-Mac Lane complex K(G,n) extends over X. These properties giv...
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متن کاملOn Definable Galois Groups and the Strong Canonical Base Property
In [3], Hrushovski and the authors proved, in a certain finite rank environment, that rigidity of definable Galois groups implies that T has the canonical base property in a strong form; “ internality to” being replaced by “algebraicity in”. In the current paper we give a reasonably robust definition of the “strong canonical base property” in a rather more general finite rank context than [3], ...
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ژورنال
عنوان ژورنال: The Bulletin of Symbolic Logic
سال: 2017
ISSN: 1079-8986,1943-5894
DOI: 10.1017/bsl.2017.2