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Keywords
Cardinal Invariants Small forcing square Uniformly homogeneous Coherent tree GMA Ascent Path Nonspecial tree Cohen real Was Ulam right? Monotonically far Partition relations for trees Universal Sequences Microscopic Approach Luzin set regressive Souslin tree Selective Ultrafilter Forcing weak diamond Successor of Singular Cardinal club_AD Non-saturation Axiom R Aronszajn tree Kurepa Hypothesis Local Club Condensation. Postprocessing function Shelah's Strong Hypothesis Hereditarily Lindelöf space Chromatic number Strongly Luzin set Reduced Power Reflecting stationary set unbounded function approachability ideal middle diamond Lipschitz reduction Successor of Regular Cardinal transformations Knaster Rock n' Roll Prevalent singular cardinals projective Boolean algebra free Boolean algebra Generalized Clubs Open Access Vanishing levels Interval topology on trees super-Souslin tree Rado's conjecture Diamond Hedetniemi's conjecture coloring number O-space Jonsson cardinal xbox Singular cofinality Foundations Ineffable cardinal Almost Souslin Strong coloring Intersection model specializable Souslin tree square principles reflection principles perfectly normal b-scale nonmeager set 54G20 Sigma-Prikry Distributive tree Fat stationary set higher Baire space Poset Subnormal ideal Almost countably chromatic Cardinal function Uniformization Fodor-type reflection PFA positive partition relation Minimal Walks Respecting tree L-space Subadditive very good scale Erdos Cardinal Antichain P-Ideal Dichotomy Closed coloring OCA Almost-disjoint family Iterated forcing Partition Relations Well-behaved magma Forcing with side conditions Filter reflection free Souslin tree Souslin Tree S-Space ccc strongly bounded groups Chang's conjecture full tree Amenable C-sequence Sakurai's Bell inequality Diamond for trees countably metacompact Entangled linear order Subtle cardinal Absoluteness Rainbow sets stick Club Guessing diamond star SNR Strongly compact cardinal Analytic sets Dushnik-Miller Generalized descriptive set theory Greatly Mahlo Whitehead Problem Prikry-type forcing Knaster and friends incompactness Dowker space Large Cardinals sap tensor product graph stationary reflection Slim tree Mandelbrot set weak Kurepa tree Martin's Axiom Precaliber Countryman line Square-Brackets Partition Relations Fast club ZFC construction Subtle tree property Erdos-Hajnal graphs Parameterized proxy principle C-sequence Ramsey theory over partitions Forcing Axioms polarized partition relation indecomposable filter Singular cardinals combinatorics Ascending path Sierpinski's onto mapping principle PFA(S)[S] AIM forcing weak square Diamond-sharp Weakly compact cardinal Uniformly coherent Constructible Universe Ulam matrix Ostaszewski square Commutative cancellative semigroups Singular Density stationary hitting Commutative projection system HOD Hindman's Theorem
Tag Archives: countably metacompact
The power of trees
Joint work with Ari Meir Brodsky and Shira Yadai. Abstract. We give two consistent constructions of trees $T$ whose finite power $T^{n+1}$ is sharply different from $T^n$: An $\aleph_1$-tree $T$ whose interval topology $X_T$ is perfectly normal, but $(X_T)^2$ is … Continue reading →
Posted in Publications, Topology
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Tagged 03E35, 54B10, 54D15, 54D20, 54F05, Almost Souslin, countably metacompact, diamond star, Interval topology on trees, Nonspecial tree, Parameterized proxy principle, perfectly normal
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1 Comment
Diamond on ladder systems and countably metacompact topological spaces
Joint work with Rodrigo Rey Carvalho and Tanmay Inamdar. Abstract. Leiderman and Szeptycki proved that a single Cohen real introduces a ladder system $L$ over $\aleph_1$ for which the space $X_L$ is not a $\Delta$-space. They asked whether there is … Continue reading →
Posted in Preprints, Topology
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Tagged 03E05, 54G20, C-sequence, countably metacompact, Diamond, middle diamond, Open Access, weak diamond, ZFC construction
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3 Comments
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 →
Posted in Squares and Diamonds, Topology
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Tagged club_AD, countably metacompact, Dowker space, Luzin set, stick
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1 Comment
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
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Tagged club_AD, countably metacompact, Dowker space, O-space, regressive Souslin tree, S-Space, Souslin Tree, Vanishing levels
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2 Comments
