Archives
Keywords
Small forcing Coherent tree Martin's Axiom free Boolean algebra Antichain Uniformly homogeneous Selective Ultrafilter club_AD Fat stationary set Absoluteness Cardinal function Almost countably chromatic HOD Countryman line Interval topology on trees Subadditive tensor product graph Distributive tree full tree Slim tree Generalized descriptive set theory Dushnik-Miller Minimal Walks Ramsey theory over partitions Filter reflection nonmeager set Iterated forcing Ineffable cardinal super-Souslin tree Entangled linear order square principles xbox Lipschitz reduction Jonsson cardinal SNR stationary reflection OCA Whitehead Problem incompactness PFA Hedetniemi's conjecture free Souslin tree ccc transformations Well-behaved magma Weakly compact cardinal weak Kurepa tree diamond star Strong coloring Diamond-sharp reflection principles Commutative cancellative semigroups Dowker space Precaliber coloring number PFA(S)[S] Non-saturation Generalized Clubs stationary hitting Hereditarily Lindelöf space sap Singular Density indecomposable filter Subtle tree property Singular cofinality Ascending path L-space Successor of Singular Cardinal stick Local Club Condensation. Strongly compact cardinal Postprocessing function Almost Souslin Vanishing levels weak square Greatly Mahlo ZFC construction regressive Souslin tree Almost-disjoint family Chromatic number Chang's conjecture Mandelbrot set Rainbow sets Intersection model Microscopic Approach Universal Sequences Forcing Axioms Knaster Partition relations for trees O-space Parameterized proxy principle Club Guessing Reflecting stationary set Ostaszewski square Amenable C-sequence Prevalent singular cardinals higher Baire space Kurepa Hypothesis Strongly Luzin set b-scale weak diamond Knaster and friends Cardinal Invariants Closed coloring 54G20 Analytic sets Hindman's Theorem Sakurai's Bell inequality middle diamond Was Ulam right? countably metacompact Diamond for trees AIM forcing positive partition relation Fodor-type reflection Erdos-Hajnal graphs Foundations Respecting tree Poset Square-Brackets Partition Relations Rock n' Roll Singular cardinals combinatorics unbounded function Constructible Universe projective Boolean algebra Subnormal ideal strongly bounded groups Nonspecial tree Uniformization Aronszajn tree Diamond Axiom R Partition Relations P-Ideal Dichotomy C-sequence Monotonically far very good scale polarized partition relation GMA Cohen real Erdos Cardinal Open Access Rado's conjecture perfectly normal Uniformly coherent square Shelah's Strong Hypothesis Souslin Tree Sigma-Prikry Forcing with side conditions approachability ideal specializable Souslin tree Luzin set Forcing Large Cardinals Successor of Regular Cardinal Commutative projection system S-Space Ascent Path Fast club Prikry-type forcing Subtle cardinal Ulam matrix Sierpinski's onto mapping principle Reduced Power
Tag Archives: Rainbow sets
Prolific Souslin trees
In a paper from 1971, Erdos and Hajnal asked whether (assuming CH) every coloring witnessing $\aleph_1\nrightarrow[\aleph_1]^2_3$ has a rainbow triangle. The negative solution was given in a 1975 paper by Shelah, and the proof and relevant definitions may be found … Continue reading
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 $f:A\rightarrow B$ is said to … Continue reading
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 $\theta$ admits a naturally defined function … Continue reading
