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