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