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On BPI Restricted to Boolean Algebras of Size Continuum

Eric Hall, Kyriakos Keremedis (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

(i) The statement P(ω) = “every partition of ℝ has size ≤ |ℝ|” is equivalent to the proposition R(ω) = “for every subspace Y of the Tychonoff product 2 ( ω ) the restriction |Y = Y ∩ B: B ∈ of the standard clopen base of 2 ( ω ) to Y has size ≤ |(ω)|”. (ii) In ZF, P(ω) does not imply “every partition of (ω) has a choice set”. (iii) Under P(ω) the following two statements are equivalent: (a) For every Boolean algebra of size ≤ |ℝ| every filter can be extended to an ultrafilter. (b) Every Boolean algebra of...

On CCC boolean algebras and partial orders

András Hajnal, István Juhász, Zoltán Szentmiklóssy (1997)

Commentationes Mathematicae Universitatis Carolinae

We partially strengthen a result of Shelah from [Sh] by proving that if κ = κ ω and P is a CCC partial order with e.g. | P | ≤ κ + ω (the ω th successor of κ ) and | P | ≤ 2 κ then P is κ -linked.

On fields and ideals connected with notions of forcing

W. Kułaga (2006)

Colloquium Mathematicae

We investigate an algebraic notion of decidability which allows a uniform investigation of a large class of notions of forcing. Among other things, we show how to build σ-fields of sets connected with Laver and Miller notions of forcing and we show that these σ-fields are closed under the Suslin operation.

On generalized derivations of partially ordered sets

Ahmed Y. Abdelwanis, Abdelkarim Boua (2019)

Communications in Mathematics

Let P be a poset and d be a derivation on P . In this research, the notion of generalized d -derivation on partially ordered sets is presented and studied. Several characterization theorems on generalized d -derivations are introduced. The properties of the fixed points based on the generalized d -derivations are examined. The properties of ideals and operations related with generalized d -derivations are studied.

On linear operators strongly preserving invariants of Boolean matrices

Yizhi Chen, Xian Zhong Zhao (2012)

Czechoslovak Mathematical Journal

Let 𝔹 k be the general Boolean algebra and T a linear operator on M m , n ( 𝔹 k ) . If for any A in M m , n ( 𝔹 k ) ( M n ( 𝔹 k ) , respectively), A is regular (invertible, respectively) if and only if T ( A ) is regular (invertible, respectively), then T is said to strongly preserve regular (invertible, respectively) matrices. In this paper, we will give complete characterizations of the linear operators that strongly preserve regular (invertible, respectively) matrices over 𝔹 k . Meanwhile, noting that a general Boolean algebra 𝔹 k is isomorphic...

On Marczewski-Burstin representable algebras

Marek Balcerzak, Artur Bartoszewicz, Piotr Koszmider (2004)

Colloquium Mathematicae

We construct algebras of sets which are not MB-representable. The existence of such algebras was previously known under additional set-theoretic assumptions. On the other hand, we prove that every Boolean algebra is isomorphic to an MB-representable algebra of sets.

On maximal QROBDD’s of boolean functions

Jean-Francis Michon, Jean-Baptiste Yunès, Pierre Valarcher (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worst-case” ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer).

On maximal QROBDD's of Boolean functions

Jean-Francis Michon, Jean-Baptiste Yunès, Pierre Valarcher (2010)

RAIRO - Theoretical Informatics and Applications

We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worst-case” ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer).

Currently displaying 241 – 260 of 467