Quasiminimal structures and excellence
نویسندگان
چکیده
منابع مشابه
On quasiminimal excellent classes
A careful exposition of Zilber’s quasiminimal excellent classes and their categoricity is given, leading to two new results: the Lω1,ω(Q)definability assumption may be dropped, and each class is determined by its model of dimension א0. Boris Zilber developed quasiminimal excellent classes in [Zil05], in order to prove that his conjectural description of complex exponentiation was categorical. T...
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We propose the notion of a quasiminimal abstract elementary class (AEC). This is an AEC satisfying four semantic conditions: countable Löwenheim-Skolem-Tarski number, existence of a prime model, closure under intersections, and uniqueness of the generic orbital type over every countable model. We exhibit a correspondence between Zilber’s quasiminimal pregeometry classes and quasiminimal AECs: a...
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We consider the quasiminima of the energy functional Z Ω A(x,∇u) + F (x, u) dx , where A(x,∇u) ∼ |∇u| and F is a double-well potential. We show that the Lipschitz quasiminima, which satisfy an equipartition of energy condition, possess density estimates of Caffarelli-Cordoba-type, that is, roughly speaking, the complement of their interfaces occupies a positive density portion of balls of large...
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We show that there exists a universal subshift having only a finite number of minimal subsystems, refuting a conjecture in [Delvenne, Kůrka, Blondel, ’05]. We then introduce the still smaller class of quasiminimal subshifts, having finitely many subsystems in total. With N-actions, their theory essentially reduces to the theory of minimal systems, but with Zactions, the class is much larger. We...
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Let u denote a quasiminimal surface (QMS) bounded by a polygon ? 2 IR q (q 2) with N+3 distinct vertices in the sense of Shiiman. A linear nite element method is presented for the approximation of u. Furthermore, an error estimation in terms of the angles at the vertices of ? and some examples of computed quasiminimal surfaces are given.
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2013
ISSN: 0024-6093
DOI: 10.1112/blms/bdt076