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diamond star Square-Brackets Partition Relations Strongly Luzin set OCA Jonsson cardinal Partition relations for trees Mandelbrot set Microscopic Approach Hedetniemi's conjecture Forcing Successor of Singular Cardinal Selective Ultrafilter Chang's conjecture Rock n' Roll Slim tree Was Ulam right? unbounded function Generalized Clubs very good scale Strongly compact cardinal stationary hitting Cohen real Greatly Mahlo middle diamond xbox Souslin Tree transformations Cardinal Invariants Martin's Axiom Small forcing square principles Fast club perfectly normal Closed coloring Local Club Condensation. Reflecting stationary set b-scale weak square Ineffable cardinal Nonspecial tree PFA Ascending path Sigma-Prikry ZFC construction nonmeager set Uniformization Hereditarily Lindelöf space club_AD Erdos Cardinal C-sequence free Boolean algebra Aronszajn tree Entangled linear order Well-behaved magma Dushnik-Miller Parameterized proxy principle O-space GMA Postprocessing function Open Access Partition Relations Iterated forcing Antichain Minimal Walks Analytic sets Whitehead Problem Countryman line Forcing Axioms L-space Universal Sequences Kurepa Hypothesis Generalized descriptive set theory Subnormal ideal Prikry-type forcing Fodor-type reflection weak diamond indecomposable filter Knaster and friends incompactness SNR HOD Uniformly homogeneous Hindman's Theorem polarized partition relation Filter reflection Coherent tree Large Cardinals Chromatic number 54G20 approachability ideal ccc Weakly compact cardinal regressive Souslin tree Respecting tree coloring number Axiom R Sierpinski's onto mapping principle Almost Souslin Almost-disjoint family reflection principles stationary reflection Singular cofinality Forcing with side conditions Monotonically far higher Baire space Singular Density Distributive tree Absoluteness square Erdos-Hajnal graphs free Souslin tree Diamond Cardinal function Rainbow sets Commutative cancellative semigroups Diamond for trees Poset Singular cardinals combinatorics AIM forcing Intersection model S-Space Vanishing levels Foundations Strong coloring stick countably metacompact super-Souslin tree Knaster Lipschitz reduction tensor product graph Reduced Power Interval topology on trees Commutative projection system weak Kurepa tree Rado's conjecture specializable Souslin tree full tree projective Boolean algebra Dowker space Almost countably chromatic PFA(S)[S] Subtle cardinal Fat stationary set Uniformly coherent Ulam matrix positive partition relation strongly bounded groups sap Diamond-sharp Subtle tree property Ostaszewski square Amenable C-sequence Non-saturation Subadditive Sakurai's Bell inequality Successor of Regular Cardinal Shelah's Strong Hypothesis Luzin set Club Guessing Precaliber Ascent Path Prevalent singular cardinals Ramsey theory over partitions P-Ideal Dichotomy Constructible Universe
Tag Archives: 54B10
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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