共查询到20条相似文献,搜索用时 15 毫秒
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We prove that each computable Boolean algebra has a computable presentation in which for every computable family of automorphisms the set of atoms moved by at least one of its members is finite. This implies that each computable atomic Boolean algebra has a computable presentation in which its every computable family of automorphisms is finite. The priority argument is not used in the proof. 相似文献
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We prove a general theorem that allows us to pass from a hyperarithmetical Boolean algebra with a distinguished ideal to some computable Boolean algebra connected with the former by natural algebraic operations. Some examples are given. 相似文献
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本文研究IMTL代数M上的索布尔滤子的运算性质。令FB(M)为膨上全体素布尔滤子集,FB(M)=FB(M)∪{φ},通过在集合FB(M)引进格并、交运算和逆序对合对应,证明了FB(M)构成一个拟布黎代数。进一步在FB(M)可定义一个伴随对,证明FB(M)也构成一个剩余格。 相似文献
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Computable Homogeneous Boolean Algebras and a Metatheorem 总被引:1,自引:0,他引:1
P. E. Alaev 《Algebra and Logic》2004,43(2):73-87
We consider computable homogeneous Boolean algebras. Previously, countable homogeneous Boolean algebras have been described up to isomorphism and a simple criterion has been found for the existence of a strongly constructive (decidable) isomorphic copy for such. We propose a natural criterion for the existence of a constructive (computable) isomorphic copy. For this, a new hierarchy of
-computable functions and sets is introduced, which is more delicate than Feiner's. Also, a metatheorem is proved connecting computable Boolean algebras and their hyperarithmetical quotient algebras. 相似文献
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For an infinite cardinal K a stronger version of K-distributivity for Boolean algebras, called k-partition completeness, is defined and investigated (e. g. every K-Suslin algebra is a K-partition complete Boolean algebra). It is shown that every k-partition complete Boolean algebra is K-weakly representable, and for strongly inaccessible K these concepts coincide. For regular K ≥ u, it is proved that an atomless K-partition complete Boolean algebra is an updirected union of basic K-tree algebras. Using K-partition completeness, the concept of γ-almost compactness is introduced for γ ≥ K. For strongly inaccessible K we show that K is K-almost compact iff K is weakly compact, and if K is 2K-almost compact, then K is measurable. Further K is strongly compact iff it is γ-almost compact for all γ ≥ K. 相似文献
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We describe the families of superatomic Boolean algebras which have a computable numbering. We define the notion of majorizability and establish a criterion that is formulated only on using algorithmic terms and majorizability. We give some examples showing that the condition of majorizability is essential. We also prove some criterion for the existence of a computable numbering for a family of -atomic algebras ( is a computable ordinal). 相似文献
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We show that every computable relation on a computable Boolean algebra
is either definable by a quantifier-free formula with constants from
(in which case it is obviously intrinsically computable) or has infinite degree spectrum. 相似文献
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We study sequential convergences defined on a Boolean algebra by systems of maximal filters. We describe the order properties of the system of all such convergences. We introduce the category of 2-generated convergence Boolean algebras and generalize the construction of Novak sequential envelope to such algebras. 相似文献
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John L. Bell 《Mathematical Logic Quarterly》1999,45(1):135-143
Some aspects of the theory of Boolean algebras and distributive lattices–in particular, the Stone Representation Theorems and the properties of filters and ideals–are analyzed in a constructive setting. 相似文献
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The Rudin‐Keisler ordering of ultrafilters is extended to complete Boolean algebras and characterised in terms of elementary embeddings of Boolean ultrapowers. The result is applied to show that the Rudin‐Keisler poset of some atomless complete Boolean algebras is nontrivial. 相似文献
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Regina Aragn 《Mathematical Logic Quarterly》1995,41(4):485-504
We consider the theory Thprin of Boolean algebras with a principal ideal, the theory Thmax of Boolean algebras with a maximal ideal, the theory Thac of atomic Boolean algebras with an ideal where the supremum of the ideal exists, and the theory Thsa of atomless Boolean algebras with an ideal where the supremum of the ideal exists. First, we find elementary invariants for Thprin and Thsa. If T is a theory in a first order language and α is a linear order with least element, then we let Sentalg(T) be the Lindenbaum-Tarski algebra with respect to T, and we let intalg(α) be the interval algebra of α. Using rank diagrams, we show that Sentalg(Thprin) ? intalg(ω4), Sentalg(Thmax) ? intalg(ω3) ? Sentalg(Thac), and Sentalg(Thsa) ? intalg(ω2 + ω2). For Thmax and Thac we use Ershov's elementary invariants of these theories. We also show that the algebra of formulas of the theory Tx of Boolean algebras with finitely many ideals is atomic. 相似文献
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Markus Huberich 《Mathematical Logic Quarterly》1996,42(1):172-174
We show that for every uncountable regular κ and every κ-complete Boolean algebra B of density ≤ κ there is a filter F ? B such that the number of partitions of length < modulo κF is ≤2<κ. We apply this to Boolean algebras of the form P(X)/I, where I is a κ-complete κ-dense ideal on X. Mathematics Subject Classification: 06E05, 03C20. 相似文献
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This note discusses the topological necessary and sufficient conditions for a locally compact connected group to admit a Gaussian measure that is absolutely continuous with respect to Haar measure. 相似文献
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We propose a definition of weak o‐minimality for structures expanding a Boolean algebra. We study this notion, in particular we show that there exist weakly o‐minimal non o‐minimal examples in this setting. 相似文献
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Let (A, T) be a locally A-pseudoconvex algebra over
or
. We define a new topology m(T) on A which is the weakest among all m-pseudoconvex topologies on A stronger than T. We describe a family of non-homogeneous seminorms on A which defines the topology m(T). 相似文献
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In this paper, the (weak) Boolean representation of R0‐algebras are investigated. In particular, we show that directly indecomposable R0‐algebras are equivalent to local R0‐algebras and any nontrivial R0‐algebra is representable as a weak Boolean product of local R0‐algebras (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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陈露 《数学的实践与认识》2010,40(18)
在布尔代数中引入了的直觉T-S模糊子代数和直觉T-S模糊理想的概念,给出了布尔代数的直觉T-S模糊子代数的两个等价定义,进一步讨论了它们的性质.证明了布尔代数的两个直觉T-S模糊子代数(理想)的模交与直积也是直觉T-S模糊子代数(理想). 相似文献
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设L是Banach空间X上的原子Boolean子空间格,δ是algL的任一导子,则存在X中的一个稠定线性算子T,使得δ(A)=AT—TA(A∈algL)在T的定义域D(T)上成立.另外,如果L还是一个有限格,并且对L的任一原子L,L+L'闭,则δ是连续的和内的. 相似文献