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Ramsey theory over partitions Rado's conjecture Strongly Luzin set Knaster and friends ZFC construction diamond star club_AD OCA weak diamond Large Cardinals Reflecting stationary set HOD super-Souslin tree Martin's Axiom Successor of Singular Cardinal Analytic sets Closed coloring Subadditive Reduced Power Ostaszewski square Fat stationary set square principles full tree Absoluteness Intersection model Almost-disjoint family Uniformly coherent Partition Relations tensor product graph Chang's conjecture stationary hitting nonmeager set Diamond for trees Nonspecial tree O-space incompactness Axiom R Generalized descriptive set theory Strong coloring S-Space Erdos Cardinal Fast club Subtle tree property Subtle cardinal Kurepa Hypothesis Ascent Path P-Ideal Dichotomy Open Access Singular cofinality Sakurai's Bell inequality Non-saturation Diamond-sharp Generalized Clubs PFA(S)[S] Prikry-type forcing transformations Poset Sigma-Prikry GMA specializable Souslin tree Square-Brackets Partition Relations Respecting tree C-sequence Fodor-type reflection Commutative projection system Hereditarily Lindelöf space Distributive tree Antichain Singular cardinals combinatorics projective Boolean algebra very good scale Local Club Condensation. Constructible Universe free Souslin tree Hindman's Theorem 54G20 Lipschitz reduction Postprocessing function stationary reflection Cohen real coloring number Rock n' Roll Diamond b-scale Successor of Regular Cardinal Selective Ultrafilter sap Ineffable cardinal unbounded function reflection principles Prevalent singular cardinals strongly bounded groups Weakly compact cardinal Iterated forcing Well-behaved magma approachability ideal Countryman line Small forcing Minimal Walks Was Ulam right ccc regressive Souslin tree PFA higher Baire space Forcing Axioms Almost countably chromatic square Vanishing levels Cardinal function Club Guessing Foundations Commutative cancellative semigroups Souslin Tree Sierpinski's onto mapping principle Knaster Subnormal ideal Amenable C-sequence weak Kurepa tree Precaliber Dowker space Ulam matrix Mandelbrot set Rainbow sets Uniformly homogeneous SNR Slim tree Universal Sequences Greatly Mahlo L-space stick Strongly compact cardinal Almost Souslin Chromatic number Singular Density indecomposable ultrafilter polarized partition relation weak square Dushnik-Miller countably metacompact xbox Whitehead Problem AIM forcing Erdos-Hajnal graphs middle diamond Parameterized proxy principle free Boolean algebra Hedetniemi's conjecture Aronszajn tree Microscopic Approach Jonsson cardinal Luzin set Coherent tree Forcing Shelah's Strong Hypothesis Filter reflection Cardinal Invariants Uniformization positive partition relation
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, Prikry-type forcing, ZFC construction
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A new small Dowker space
Joint work with Roy Shalev and Stevo Todorcevic. Abstract. It is proved that if there exists a Luzin set, or if either the stick principle or $\diamondsuit(\mathfrak b)$ hold, then an instance of the guessing principle $\clubsuit_{AD}$ holds at the … Continue reading
A guessing principle from a Souslin tree, with applications to topology
Joint work with Roy Shalev. Abstract. We introduce a new combinatorial principle which we call $\clubsuit_{AD}$. This principle asserts the existence of a certain multi-ladder system with guessing and almost-disjointness features, and is shown to be sufficient for carrying out … Continue reading
Posted in Publications, Souslin Hypothesis, Topology
Tagged club_AD, Dowker space, O-space, regressive Souslin tree, S-Space, Souslin Tree, Vanishing levels
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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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