Archives
Keywords
Ulam matrix Antichain Prevalent singular cardinals free Souslin tree perfectly normal AIM forcing Chromatic number Constructible Universe Sierpinski's onto mapping principle L-space specializable Souslin tree Aronszajn tree Generalized Clubs Strong coloring Hindman's Theorem Ascent Path Reflecting stationary set Microscopic Approach Diamond for trees square Rado's conjecture Successor of Singular Cardinal Selective Ultrafilter Subtle tree property Intersection model Rainbow sets 54G20 Well-behaved magma Knaster and friends Slim tree PFA(S)[S] Coherent tree O-space Entangled linear order b-scale Hereditarily Lindelöf space Whitehead Problem Successor of Regular Cardinal Greatly Mahlo Monotonically far free Boolean algebra HOD Sakurai's Bell inequality Luzin set approachability ideal Foundations Parameterized proxy principle Souslin Tree diamond star transformations Uniformly coherent Shelah's Strong Hypothesis Ascending path very good scale Erdos-Hajnal graphs Square-Brackets Partition Relations Martin's Axiom Poset Non-saturation Forcing polarized partition relation club_AD indecomposable filter Diamond stick Lipschitz reduction Cohen real ccc stationary hitting Singular cofinality Prikry-type forcing Partition Relations regressive Souslin tree OCA Closed coloring Absoluteness Chang's conjecture ZFC construction positive partition relation projective Boolean algebra Singular cardinals combinatorics super-Souslin tree Was Ulam right? weak Kurepa tree Partition relations for trees Subtle cardinal Vanishing levels nonmeager set xbox Commutative projection system Rock n' Roll unbounded function C-sequence Amenable C-sequence Commutative cancellative semigroups Filter reflection coloring number Subadditive Club Guessing Axiom R Strongly compact cardinal reflection principles Weakly compact cardinal Hedetniemi's conjecture middle diamond Diamond-sharp Almost countably chromatic incompactness Small forcing Nonspecial tree strongly bounded groups Dowker space weak diamond Cardinal function tensor product graph Knaster Postprocessing function weak square Countryman line Almost Souslin higher Baire space Uniformly homogeneous Kurepa Hypothesis Forcing Axioms Mandelbrot set GMA Generalized descriptive set theory Respecting tree Minimal Walks Sigma-Prikry Universal Sequences Jonsson cardinal square principles Interval topology on trees Ramsey theory over partitions Distributive tree Iterated forcing S-Space Singular Density Subnormal ideal Large Cardinals stationary reflection SNR sap Strongly Luzin set Open Access PFA countably metacompact P-Ideal Dichotomy Precaliber Dushnik-Miller full tree Almost-disjoint family Ostaszewski square Fat stationary set Analytic sets Cardinal Invariants Local Club Condensation. Forcing with side conditions Fast club Reduced Power Fodor-type reflection Erdos Cardinal Ineffable cardinal Uniformization
Tag Archives: reflection principles
The reflection principle $R_2$
A few years ago, in this paper, I introduced the following reflection principle: Definition. $R_2(\theta,\kappa)$ asserts that for every function $f:E^\theta_{<\kappa}\rightarrow\kappa$, there exists some $j<\kappa$ for which the following set is nonstationary: $$A_j:=\{\delta\in E^\theta_\kappa\mid f^{-1}[j]\cap\delta\text{ is nonstationary}\}.$$ I wrote there … Continue reading
Posted in Blog
Tagged reflection principles, square, stationary reflection, Weakly compact cardinal
Comments Off on The reflection principle $R_2$
The chromatic numbers of the Erdos-Hajnal graphs
Recall that a coloring $c:G\rightarrow\kappa$ of an (undirected) graph $(G,E)$ is said to be chromatic if $c(v_1)\neq c(v_2)$ whenever $\{v_1,v_2\}\in E$. Then, the chromatic number of a graph $(G,E)$ is the least cardinal $\kappa$ for which there exists a chromatic … Continue reading
Posted in Blog, Expository
Tagged Chromatic number, Erdos-Hajnal graphs, Rado's conjecture, reflection principles
14 Comments
