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