Uniform Birkhoff
نویسندگان
چکیده
منابع مشابه
Uniform Birkhoff
We show that pseudovarieties of finitely generated algebras, i.e., classes C of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure UC on the free algebra for C: the members of C then are precisely those finitely generated algebras A for which the natural mapping from the free algebra onto the term clone of A is...
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In this paper we initiate the study of Birkhoff interpolation schemes with main emphasis on the shape of the set of nodes. We concentrate here on the simplest shapes (“rectangular”). The ultimate goal is to obtain a geometrical understanding of the solvability. We present several regularity criteria, a few conjectures, with geometric interpretations, and we illustrate with many examples.
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A fundamental result in rewriting is : E |= s ≈ t ⇐⇒1 E ` s = t ⇐⇒2 s↔E t 1. is Birkhoff’s theorem expressing that semantic consequence (|=) coincides with syntactic consequence (`). 2. expresses that equality in equational logic (=) coincides with convertibility in rewriting (↔∗), a property known as logicality. We show that the result can be extended to hold for several sub-equational logics ...
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One of the most fundamental mathematical contributions of Garrett Birkhoff is the HSP theorem, which implies that a finite algebra B satisfies all equations that hold in a finite algebra A of the same signature if and only if B is a homomorphic image of a subalgebra of a finite power of A. On the other hand, if A is infinite, then in general one needs to take an infinite power in order to obtai...
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In this article, using a combination of the necessary and sufficient conditions for the almost regularity of an interpolation scheme, we will determine all plane uniform Birkhoff schemes, when the set of interpolated nodes has n elements and the set of derivatives we are interpolating with is )} 0 , 1 ( ), 0 , 0 {( = A . For the same A we will determine all rectangular Birkhoff uniform interpol...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2018
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2017.06.016