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