共查询到20条相似文献,搜索用时 15 毫秒
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Using Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ++ + ≤ λ, κ<κ = κ and 2κ = κ+, and η is an ordinal with κ+ ≤ η < κ++ and cf(η) = κ+. Then, in some cardinal‐preserving generic extension there is a superatomic Boolean algebra $\mathcal BUsing Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ++ + ≤ λ, κ<κ = κ and 2κ = κ+, and η is an ordinal with κ+ ≤ η < κ++ and cf(η) = κ+. Then, in some cardinal‐preserving generic extension there is a superatomic Boolean algebra $\mathcal B$ such that $\mathrm{ht}(\mathcal B) = \eta + 1$, $\mathrm{wd}_{\alpha }(\mathcal B) = \kappa$ for every α < η and $\mathrm{wd}_{\eta }(\mathcal B) = \lambda$(i.e., there is a locally compact scattered space with cardinal sequence 〈κ〉η??〈λ〉). Especially, $\langle {\omega }\rangle _{{\omega }_1}{}^{\smallfrown } \langle {\omega }_3\rangle$ and $\langle {\omega }_1\rangle _{{\omega }_2}{}^{\smallfrown } \langle {\omega }_4\rangle$ can be cardinal sequences of superatomic Boolean algebras. 相似文献
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Paul Howard 《Mathematical Logic Quarterly》2011,57(1):14-18
We show that it consistent with Zermelo‐Fraenkel set theory that there is an infinite, compact Boolean algebra (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Roman Wencel 《Mathematical Logic Quarterly》2012,58(3):217-235
Given an infinite Boolean algebra B, we find a natural class of $\varnothing$‐definable equivalence relations $\mathcal {E}_{B}$ such that every imaginary element from Beq is interdefinable with an element from a sort determined by some equivalence relation from $\mathcal {E}_{B}$. It follows that B together with the family of sorts determined by $\mathcal {E}_{B}$ admits elimination of imaginaries in a suitable multisorted language. The paper generalizes author's earlier results concerning definable equivalence relations and weak elimination of imaginaries for Boolean algebras, obtained in 10 . 相似文献
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Dung Le 《Annali di Matematica Pura ed Applicata》2006,185(1):133-154
A class of strongly coupled parabolic systems is investigated. Sufficient conditions on the structure of the systems are found to assure that weak solutions are bounded and that they are Hölder continuous. Together, these results give the global existence of solutions. The theory is then applied to the general Shigesada–Kawasaki–Teramoto model in population dynamics. 相似文献
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Saharon Shelah 《Algebra Universalis》2005,54(1):91-96
We show that if μ is a compact cardinal then the depth of ultraproducts of less than μ many Boolean algebras is at most μ
plus the ultraproduct of the depths of those Boolean algebras.
Received May 18, 2004; accepted in final form December 9, 2004. 相似文献
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In this work, some results related to superatomic Boolean interval algebras are presented, and proved in a topological way. Let x be an uncountable cardinal. To each I
x, we can associate a superatomic interval Boolean algebra B
I of cardinality x in such a way that the following properties are equivalent: (i) I
I
x, (ii) B
I is a quotient algebra of B
J, and (iii) there is an homomorphism f from B
J into B
I such that for every atom b of B
I, there is an atom a of B
J satisfying f(a)=b. As a corollary, there are 2
x
isomorphism types of superatomic interval Boolean algebras of cardinality x. This case is quite different from the countable one. 相似文献
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A. I. Omarov 《Siberian Mathematical Journal》1974,15(6):1004-1005
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Yafit Natani 《代数通讯》2017,45(9):3872-3885
In this paper, we investigate the basis graph of the monoid algebra of a submonoid of the monoid of mappings from N = {1,…,n} to itself, defined by a nested sequence of compositions of N. Each such monoid is a left regular band (LRB), that is, a semigroup S satisfying x2 = x and xyx = xy for all x,y∈S. This class is su?ciently rich that every path algebra of an acyclic quiver can be embedded in such a monoid algebra. The multiplication in the monoid algebra has a particularly simple quasi-multiplicative form, allowing definition over the integers. Combining this with a formula for Ext-groups for LRBs due to Margolis et al. [6], we get a simple criterion for the nested composition algebras to be hereditary. 相似文献
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A linear operatorT L(H) is called a strongly irreducible, if there is no non-trivial idempotent linear operator commuting withT. In this paper, denote the set of all strongly irreducible operators by (SI). Let
be a nest with infinite dimensional atoms,
be the nest algebra associated with
and
be the closure of
, then the following result is proved
.The projection partially supported by Chinese Natural Science Foundation and Fund of Laboratory of Nonlinear Mathematical Modeling and Methods in Fudan University in Shanghai P.R.C. 相似文献
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In this paper, we classify the irreducible ?r,n-modules over a field. 相似文献
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Martin Aigner 《Journal of Combinatorial Theory, Series B》1973,14(3):187-194
Hall's theorem on systems of distinct representatives implies the existence of matchings between two consecutive levels of a Boolean algebra. In this paper a very simple construction of such matchings is given whose induced chains are in addition symmetric. 相似文献
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The strongly irreducible operators in nest algebras 总被引:2,自引:0,他引:2
An operatorT on
is called strongly irreducible ifT does not commute with any nontrivial idempotent operator. In this paper, we first show that each nest algebra (
) has strongly irreducible operators. Secondly, we obtain a characterization of operators which can be uniquely written as a direct sum of finitely many strongly irreducible operators. Finally, we characterize the strongly irreducibility of operators in a nest algebra (
).This project was partially supported by National Natural Science Foundation of China. 相似文献