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