منابع مشابه
A Robuster Scott Rank
We give a new definition of Scott rank motivated by our main theorem: For every countable structure A and ordinal α < ω1, we have that: every automorphism orbit is Σ α -definable without parameters if and only if A has a Π α+1 Scott sentence, if and only if A is uniformly boldface ∆α-categorical. As a corollary, we show that a structure is computably categorical on a cone if and only if it is t...
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We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 in the space of bilinear maps C × C → C. This space of bilinear maps includes the matrix multiplication operator M2 for two by two matrices. We show these newly obtained polynomials do not vanish on the matrix ...
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1. PRELIMINARIES Let S be a non empty set and let a, b be elements of S. The functor a,b, ... yielding a function from N into S is defined by the condition (Def. 1). (Def. 1) Let i be a natural number. Then (i) if there exists a natural number k such that i = 2 · k, then (a,b, ...)(i) = a, and (ii) if it is not true that there exists a natural number k such that i = 2 · k, then (a,b, ...)(i) = ...
متن کاملStructures in Familiar Classes Which Have Scott Rank Ω
There are familiar examples of computable structures having various computable Scott ranks. There are also familiar structures, such as the Harrison ordering, which have Scott rank ω CK 1 + 1. Makkai [12] produced a structure of Scott rank ω CK 1 , which can be made computable [10], and simplified so that it is just a tree [4]. In the present paper, we show that there are further computable str...
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An extended formulation of a polytope P is a system of linear inequalities and equations that describe some polyhedron which can be projected onto P. Extended formulations of small size (i.e., number of inequalities) are of interest, as they allow to model corresponding optimization problems as linear programs of small sizes. In this paper, we describe several aspects and new results on the mai...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2020
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/15056