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Perfect subtree property for weakly compact cardinals
We investigate the consistency strength of the statement: κ is weakly compact and there is no tree on κ with exactly κ + many branches. We show that...
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Questions on cardinal invariants of Boolean algebras
In the book Cardinal Invariants on Boolean Algebras by J. Donald Monk many such cardinal functions are defined and studied. Among them several are...
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When is a cellular-countably-compact space, countably compact?
We continue the study of cellular-compact spaces and the larger class of cellular-countably-compact spaces. We give a number of sufficient conditions...
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On regular separable countably compact ℝ-rigid spaces
A topological space X is said to be Y -rigid if any continuous map f: X → Y is constant. In this paper we construct a number of examples of regular...
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On the additivity of strong homology for locally compact separable metric spaces
We show that it is consistent relative to a weakly compact cardinal that strong homology is additive and compactly supported within the class of...
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Compact productivity of Lindelöf-type properties
A subclass of the class of feebly Lindelöf spaces, namely the almost cellular-Lindelöf spaces, which contains the class of all cellular-Lindelöf...
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Countable Strongly Annihilated Ideals in Commutative Rings
In this paper, we introduce and study the concept of countable strongly annihilated ideal in commutative rings, in particular in rings of continuous...
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Square compactness and Lindelöf trees
We prove that every weakly square compact cardinal is a strong limit cardinal, and therefore weakly compact. We also study Aronszajn trees with no...
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Preservation of splitting families and cardinal characteristics of the continuum
We show how to construct, via forcing, splitting families that are preserved by a certain type of finite support iterations. As an application, we...
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Strongly Topological Gyrogroups with Remainders Close to Metrizable
Some results between the properties of strongly topological gyrogroups and the properties of their remainders are established. In particular, if a...
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Homomorphic images of locally compact groups acting on trees and buildings
We study analogues of Cartan decompositions of Lie groups for totally disconnected locally compact groups. It is shown using these decompositions...
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Forcing level by level equivalence and a consequence of UA
We show how Hamkins’ Gap Forcing Theorem of Hamkins (Israel J Math 125:237–252, 2001, Bull Symb Logic 5: 264–272, 1999) can be used to give an...
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Strong tree properties, Kurepa trees, and guessing models
We investigate the generalized tree properties and guessing model properties introduced by Weiß and Viale, as well as natural weakenings thereof,...
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Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms
In this series of papers we advance Ramsey theory over partitions. In this part, a correspondence between anti-Ramsey properties of partitions and...
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Strong asymptotic freeness for independent uniform variables on compact groups associated to nontrivial representations
Voiculescu discovered asymptotic freeness of independent Haar-distributed unitary matrices. Many refinements have been obtained, including strong...
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Cauchy-compact flat spacetimes with extreme BTZ
Cauchy-compact flat spacetimes with extreme BTZ are Lorentzian analogue of complete hyperbolic surfaces of finite volume. Indeed, the latter are...
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Topological Properties of the Weak and Weak \(^*\) Topologies of Function Spaces
We show that if a locally convex space (lcs) \((E,\tau )\)...