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Lipschitz reduction Knaster Fast club Uniformly coherent Kurepa Hypothesis Microscopic Approach Souslin Tree Respecting tree Shelah's Strong Hypothesis Precaliber Almost-disjoint family Commutative cancellative semigroups Sigma-Prikry free Boolean algebra Iterated forcing regressive Souslin tree Whitehead Problem Subadditive tensor product graph Monotonically far Parameterized proxy principle very good scale reflection principles Interval topology on trees middle diamond Closed coloring Cardinal function Large Cardinals AIM forcing indecomposable filter Successor of Singular Cardinal incompactness Sierpinski's onto mapping principle stationary hitting Cardinal Invariants Entangled linear order Ineffable cardinal Foundations Poset free Souslin tree Postprocessing function ZFC construction Slim tree Selective Ultrafilter specializable Souslin tree SNR Square-Brackets Partition Relations Almost Souslin Dowker space Aronszajn tree Subtle cardinal Uniformization OCA Prevalent singular cardinals weak Kurepa tree Ulam matrix HOD Amenable C-sequence Partition relations for trees Commutative projection system nonmeager set Subnormal ideal Prikry-type forcing O-space square principles Local Club Condensation. b-scale Successor of Regular Cardinal super-Souslin tree higher Baire space Uniformly homogeneous full tree Rainbow sets Was Ulam right? Absoluteness Intersection model Cohen real Greatly Mahlo coloring number Vanishing levels Fat stationary set GMA Diamond-sharp Non-saturation Minimal Walks Hedetniemi's conjecture Almost countably chromatic Dushnik-Miller Generalized descriptive set theory Chang's conjecture Singular cofinality stick Erdos-Hajnal graphs C-sequence Knaster and friends Strongly compact cardinal Ostaszewski square ccc Reduced Power S-Space square approachability ideal Subtle tree property Filter reflection Coherent tree Constructible Universe Analytic sets Countryman line Mandelbrot set perfectly normal strongly bounded groups projective Boolean algebra weak square Distributive tree countably metacompact Forcing Axioms 54G20 stationary reflection Ramsey theory over partitions Universal Sequences Luzin set PFA club_AD Rock n' Roll Singular cardinals combinatorics Hereditarily Lindelöf space Martin's Axiom Chromatic number Strongly Luzin set Generalized Clubs L-space Nonspecial tree Well-behaved magma Fodor-type reflection Club Guessing Forcing with side conditions diamond star Diamond weak diamond Jonsson cardinal xbox Axiom R Open Access Reflecting stationary set Hindman's Theorem Antichain PFA(S)[S] positive partition relation Weakly compact cardinal Rado's conjecture Ascent Path Sakurai's Bell inequality Forcing Strong coloring sap polarized partition relation Ascending path Diamond for trees P-Ideal Dichotomy Small forcing Erdos Cardinal Partition Relations transformations Singular Density unbounded function
Category Archives: Topology
40th summer conference on topology and its applications
I gave an invited talk at the General and Set-Theoretic Topology session of the 40th summer conference on topology and its applications, July 2026. Talk title: A tree-based perfectly normal space whose square is not countably metacompact. Abstract. The study … Continue reading
Posted in Invited Talks, Topology
Tagged Interval topology on trees
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A counterexample related to a theorem of Komjáth and Weiss
Joint work with Rodrigo Rey Carvalho. Abstract. In a paper from 1987, Komjath and Weiss proved that for every regular topological space $X$ of character less than $\mathfrak b$, if $X\rightarrow(\text{top }{\omega+1})^1_\omega$, then $X\rightarrow(\text{top }{\alpha})^1_\omega$ for all $\alpha<\omega_1$. In addition, … Continue reading
Posted in Partition Relations, Preprints, Topology
Tagged 03E02, 54G20, Open Access, Prikry-type forcing, ZFC construction
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On topological spaces of singular density and minimal weight
Abstract: We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the Prevalent Singular cardinals Hypothesis (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf. The assumption … Continue reading
A topological reflection principle equivalent to Shelah’s strong hypothesis
Abstract: We notice that Shelah’s Strong Hypothesis (SSH) is equivalent to the following reflection principle: Suppose $\mathbb X$ is an (infinite) first-countable space whose density is a regular cardinal, $\kappa$. If every separable subspace of $\mathbb X$ is of cardinality at most … Continue reading
Posted in Compactness, Publications, Topology
Tagged 03E04, 03E65, 54G15, Open Access, Shelah's Strong Hypothesis
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