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incompactness weak square Ostaszewski square Lipschitz reduction Souslin Tree PFA(S)[S] diamond star Erdos-Hajnal graphs Shelah's Strong Hypothesis Partition relations for trees Sierpinski's onto mapping principle b-scale transformations Entangled linear order Diamond unbounded function Universal Sequences Microscopic Approach Successor of Regular Cardinal SNR full tree higher Baire space Cohen real Forcing with side conditions Slim tree Uniformization O-space Partition Relations Open Access Ineffable cardinal Hedetniemi's conjecture Sigma-Prikry Poset weak Kurepa tree Chromatic number super-Souslin tree Greatly Mahlo Iterated forcing L-space Subtle tree property reflection principles stationary hitting Ramsey theory over partitions Singular Density positive partition relation Hindman's Theorem Ascent Path Interval topology on trees AIM forcing Generalized descriptive set theory nonmeager set Almost countably chromatic Dushnik-Miller Martin's Axiom Jonsson cardinal Dowker space indecomposable filter 54G20 approachability ideal xbox Well-behaved magma club_AD Kurepa Hypothesis HOD Prevalent singular cardinals strongly bounded groups Selective Ultrafilter Monotonically far Parameterized proxy principle OCA C-sequence Vanishing levels P-Ideal Dichotomy Luzin set Rock n' Roll Aronszajn tree Antichain ZFC construction Rainbow sets Rado's conjecture Strongly Luzin set Ascending path Commutative cancellative semigroups Cardinal function Erdos Cardinal Club Guessing Almost-disjoint family Sakurai's Bell inequality Diamond-sharp Minimal Walks Constructible Universe Ulam matrix coloring number Axiom R Countryman line Forcing Axioms Subadditive Coherent tree GMA middle diamond Large Cardinals regressive Souslin tree Small forcing Weakly compact cardinal Subnormal ideal square sap Nonspecial tree Filter reflection projective Boolean algebra Uniformly homogeneous Almost Souslin Uniformly coherent Reduced Power Absoluteness specializable Souslin tree perfectly normal polarized partition relation countably metacompact free Boolean algebra Commutative projection system ccc stick Mandelbrot set Singular cardinals combinatorics Fat stationary set S-Space Intersection model Diamond for trees Local Club Condensation. very good scale Amenable C-sequence Whitehead Problem Cardinal Invariants Singular cofinality Square-Brackets Partition Relations PFA Strong coloring tensor product graph Postprocessing function stationary reflection Hereditarily Lindelöf space Generalized Clubs Knaster Forcing Fodor-type reflection free Souslin tree Analytic sets Successor of Singular Cardinal Subtle cardinal Fast club Distributive tree Knaster and friends Closed coloring Precaliber square principles Non-saturation Was Ulam right? Chang's conjecture Prikry-type forcing Respecting tree Foundations Strongly compact cardinal weak diamond Reflecting stationary set
Tag Archives: stick
Strongest transformations
Joint work with Jing Zhang. Abstract. We continue our study of maps transforming high-dimensional complicated objects into squares of stationary sets. Previously, we proved that many such transformations exist in ZFC, and here we address the consistency of the strongest … Continue reading
Posted in Partition Relations, Publications
Tagged Diamond, Minimal Walks, square, Square-Brackets Partition Relations, stick, transformations, xbox
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Polychromatic colorings
These are lectures notes of two talks Dani Livne gave in our Infinite Combinatorics seminar. I did not take notes in real-time, hence, all possible mistakes here are due to myself. Recall that a function $f:A\rightarrow B$ is said to … Continue reading
