Archives
Keywords
stationary reflection weak diamond middle diamond reflection principles GMA Ostaszewski square full tree Uniformly homogeneous Entangled linear order Universal Sequences regressive Souslin tree Foundations Sigma-Prikry free Souslin tree Rado's conjecture Uniformly coherent Vanishing levels Countryman line Precaliber Martin's Axiom Constructible Universe Partition Relations positive partition relation S-Space Shelah's Strong Hypothesis square Partition relations for trees Diamond-sharp Generalized descriptive set theory Dushnik-Miller Ineffable cardinal coloring number Non-saturation P-Ideal Dichotomy Jonsson cardinal Diamond for trees Aronszajn tree Nonspecial tree Reflecting stationary set Luzin set Fodor-type reflection Greatly Mahlo Forcing Closed coloring Postprocessing function stationary hitting Forcing with side conditions Subtle cardinal PFA(S)[S] Open Access Monotonically far Rock n' Roll Iterated forcing Commutative projection system diamond star C-sequence Poset AIM forcing Diamond Local Club Condensation. Large Cardinals Minimal Walks Rainbow sets Slim tree Analytic sets L-space Weakly compact cardinal Selective Ultrafilter strongly bounded groups Chromatic number Singular cardinals combinatorics countably metacompact Ulam matrix Knaster incompactness Chang's conjecture Commutative cancellative semigroups Strong coloring Strongly Luzin set Hereditarily Lindelöf space Sakurai's Bell inequality Erdos-Hajnal graphs projective Boolean algebra Axiom R ZFC construction Subnormal ideal Was Ulam right? Prikry-type forcing unbounded function Square-Brackets Partition Relations Kurepa Hypothesis Antichain b-scale nonmeager set Filter reflection approachability ideal Mandelbrot set xbox Well-behaved magma Almost Souslin Generalized Clubs Cardinal function Strongly compact cardinal Reduced Power Sierpinski's onto mapping principle Small forcing Parameterized proxy principle Almost-disjoint family Almost countably chromatic Singular cofinality ccc perfectly normal SNR stick Cohen real Amenable C-sequence very good scale Successor of Regular Cardinal super-Souslin tree specializable Souslin tree Uniformization Ascending path Respecting tree Dowker space O-space Erdos Cardinal Ramsey theory over partitions transformations tensor product graph Hindman's Theorem Subtle tree property 54G20 Microscopic Approach weak square club_AD Absoluteness Distributive tree polarized partition relation Club Guessing Knaster and friends Souslin Tree indecomposable filter Fat stationary set OCA sap higher Baire space HOD Forcing Axioms free Boolean algebra Lipschitz reduction Hedetniemi's conjecture Subadditive Prevalent singular cardinals Coherent tree square principles Cardinal Invariants weak Kurepa tree Fast club Successor of Singular Cardinal Intersection model Interval topology on trees Ascent Path Whitehead Problem Singular Density PFA
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
Comments Off on 40th summer conference on topology and its applications
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
Comments Off on A counterexample related to a theorem of Komjáth and Weiss
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
Comments Off on A topological reflection principle equivalent to Shelah’s strong hypothesis
