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On partial orderings having precalibre-ℵ₁ and fragments of Martin's axiom

Joan Bagaria, Saharon Shelah (2016)

Fundamenta Mathematicae

We define a countable antichain condition (ccc) property for partial orderings, weaker than precalibre-ℵ₁, and show that Martin's axiom restricted to the class of partial orderings that have the property does not imply Martin's axiom for σ-linked partial orderings. This yields a new solution to an old question of the first author about the relative strength of Martin's axiom for σ-centered partial orderings together with the assertion that every Aronszajn tree is special. We also answer a question...

On partitions of lines and space

Paul Erdös, Steve Jackson, R. Mauldin (1994)

Fundamenta Mathematicae

We consider a set, L, of lines in ℝ n and a partition of L into some number of sets: L = L 1 ∪ . . . ∪ L p . We seek a corresponding partition ℝ n = S 1 ∪ . . . ∪ S p such that each line l in L i meets the set S i in a set whose cardinality has some fixed bound, ω τ . We determine equivalences between the bounds on the size of the continuum, 2 ω ≤ ω θ , and some relationships between p, ω τ and ω θ .

On permutographs

Thomas, Gerhard G. (1982)

Proceedings of the 10th Winter School on Abstract Analysis

On powers of Lindelöf spaces

Isaac Gorelic (1994)

Commentationes Mathematicae Universitatis Carolinae

We present a forcing construction of a Hausdorff zero-dimensional Lindelöf space X whose square X 2 is again Lindelöf but its cube X 3 has a closed discrete subspace of size 𝔠 + , hence the Lindelöf degree L ( X 3 ) = 𝔠 + . In our model the Continuum Hypothesis holds true. After that we give a description of a forcing notion to get a space X such that L ( X n ) = ℵ 0 for all positive integers n , but L ( X ℵ 0 ) = 𝔠 + = ℵ 2 .

On problems of databases over a fixed infinite universe

Oleg Belegradek, Alexei Stolboushkin, Michael Taitslin (1999)

Banach Center Publications

In the relational model of databases a database state is thought of as a finite collection of relations between elements. For many applications it is convenient to pre-fix an infinite domain where the finite relations are going to be defined. Often, we also fix a set of domain functions and/or relations. These functions/relations are infinite by their nature. Some special problems arise if we use such an approach. In the paper we discuss some of the problems. We show that there exists a recursive...

On projectional skeletons in Vašák spaces

Ondřej F. K. Kalenda (2017)

Commentationes Mathematicae Universitatis Carolinae

We provide an alternative proof of the theorem saying that any Vašák (or, weakly countably determined) Banach space admits a full 1 -projectional skeleton. The proof is done with the use of the method of elementary submodels and is comparably simple as the proof given by W. Kubiś (2009) in case of weakly compactly generated spaces.

On pseudo BE-algebras

Rajab Ali Borzooei, Arsham Borumand Saeid, Akbar Rezaei, Akefe Radfar, Reza Ameri (2013)

Discussiones Mathematicae - General Algebra and Applications

In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and pre-image of a pseudo filter is also a pseudo filter. Furthermore, the notion of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets.

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