Archives
Keywords
Analytic sets Subtle cardinal PFA(S)[S] Generalized descriptive set theory SNR ccc Weakly compact cardinal sap Countryman line positive partition relation GMA Hedetniemi's conjecture xbox Whitehead Problem Strongly Luzin set Sigma-Prikry Vanishing levels Poset Kurepa Hypothesis Uniformly homogeneous Chromatic number OCA Iterated forcing Shelah's Strong Hypothesis Reflecting stationary set Closed coloring indecomposable ultrafilter Partition Relations Foundations Singular cardinals combinatorics weak diamond stationary hitting Parameterized proxy principle Dowker space AIM forcing Subnormal ideal Cardinal function higher Baire space Martin's Axiom square principles Mandelbrot set Coherent tree L-space Cardinal Invariants full tree Commutative cancellative semigroups Antichain Commutative projection system Minimal Walks incompactness Ostaszewski square Aronszajn tree Small forcing unbounded function Open Access Cohen real Sakurai's Bell inequality HOD Strong coloring free Boolean algebra polarized partition relation Lipschitz reduction specializable Souslin tree Precaliber very good scale S-Space Large Cardinals Absoluteness Knaster and friends Postprocessing function stationary reflection O-space Diamond-sharp Fast club Intersection model regressive Souslin tree Greatly Mahlo Respecting tree Subadditive Well-behaved magma Was Ulam right? Souslin Tree Rainbow sets Local Club Condensation. Ascent Path Fat stationary set Slim tree square Almost countably chromatic Distributive tree Strongly compact cardinal Almost-disjoint family Dushnik-Miller tensor product graph Universal Sequences Reduced Power Axiom R Singular Density Filter reflection coloring number Ramsey theory over partitions Almost Souslin Ulam matrix P-Ideal Dichotomy Forcing Axioms Nonspecial tree weak Kurepa tree Fodor-type reflection nonmeager set PFA Ineffable cardinal Square-Brackets Partition Relations Prikry-type forcing Subtle tree property club_AD Rado's conjecture free Souslin tree Uniformization C-sequence Erdos Cardinal projective Boolean algebra Uniformly coherent reflection principles transformations Rock n' Roll Constructible Universe Non-saturation stick Chang's conjecture Hereditarily Lindelöf space Luzin set Successor of Singular Cardinal Amenable C-sequence super-Souslin tree Selective Ultrafilter approachability ideal Diamond Forcing Sierpinski's onto mapping principle Club Guessing Erdos-Hajnal graphs Hindman's Theorem Generalized Clubs middle diamond Jonsson cardinal 54G20 countably metacompact Successor of Regular Cardinal Prevalent singular cardinals Singular cofinality strongly bounded groups Knaster weak square diamond star Diamond for trees ZFC construction Microscopic Approach b-scale
Tag Archives: Rainbow sets
Prolific Souslin trees
In a paper from 1971, Erdos and Hajnal asked whether (assuming CH) every coloring witnessing
Posted in Blog, Expository
Tagged Rainbow sets, Souslin Tree, Square-Brackets Partition Relations
Leave a comment
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
Comparing rectangles with squares through rainbow sets
In Todorcevic’s class last week, he proved all the results of Chapter 8 from his Walks on Ordinals book, up to (and including) Theorem 8.1.11. The upshots are as follows: Every regular infinite cardinal