Archives
Keywords
Prikry-type forcing Poset Ostaszewski square Analytic sets Sierpinski's onto mapping principle SNR Coherent tree stationary hitting Generalized descriptive set theory weak square Weakly compact cardinal Almost Souslin middle diamond nonmeager set tensor product graph diamond star Rainbow sets Knaster and friends Knaster Fat stationary set Reflecting stationary set Hedetniemi's conjecture Subtle tree property Cohen real 54G20 Minimal Walks regressive Souslin tree free Boolean algebra countably metacompact Fast club Universal Sequences PFA(S)[S] Closed coloring Generalized Clubs Kurepa Hypothesis Greatly Mahlo Selective Ultrafilter Small forcing strongly bounded groups Uniformly coherent Open Access full tree Was Ulam right? Almost countably chromatic transformations Lipschitz reduction higher Baire space indecomposable filter AIM forcing S-Space Forcing Ascent Path Local Club Condensation. C-sequence Luzin set Strong coloring Erdos-Hajnal graphs Non-saturation coloring number Sakurai's Bell inequality square projective Boolean algebra Parameterized proxy principle Almost-disjoint family unbounded function Prevalent singular cardinals Countryman line Uniformly homogeneous HOD L-space approachability ideal Filter reflection Subadditive Fodor-type reflection Postprocessing function Square-Brackets Partition Relations Constructible Universe Singular cofinality Cardinal Invariants Chromatic number Sigma-Prikry Aronszajn tree Diamond for trees square principles Strongly Luzin set GMA stationary reflection b-scale Souslin Tree O-space Whitehead Problem weak Kurepa tree Iterated forcing Foundations Partition Relations ccc weak diamond Dushnik-Miller Absoluteness free Souslin tree Distributive tree Antichain Ineffable cardinal Rado's conjecture Ulam matrix club_AD Respecting tree polarized partition relation Cardinal function Mandelbrot set Hereditarily Lindelöf space Singular Density Commutative projection system Chang's conjecture super-Souslin tree Singular cardinals combinatorics Subnormal ideal stick Diamond-sharp Microscopic Approach incompactness Shelah's Strong Hypothesis ZFC construction Dowker space Club Guessing xbox Reduced Power Martin's Axiom Subtle cardinal sap Nonspecial tree Commutative cancellative semigroups reflection principles Jonsson cardinal Vanishing levels P-Ideal Dichotomy Precaliber Forcing Axioms Axiom R Strongly compact cardinal Erdos Cardinal Intersection model Ramsey theory over partitions specializable Souslin tree very good scale Hindman's Theorem Well-behaved magma PFA Large Cardinals Rock n' Roll Diamond Amenable C-sequence Successor of Regular Cardinal Uniformization Successor of Singular Cardinal Slim tree positive partition relation OCA
Category Archives: Blog
Afghan Whigs on Jimmy Fallon
Performing “I’m Her Slave” (from their album Congregation) at NBC’s studios, 22-May-2012:
The chromatic numbers of the Erdos-Hajnal graphs
Recall that a coloring
Posted in Blog, Expository
Tagged Chromatic number, Erdos-Hajnal graphs, Rado's conjecture, reflection principles
13 Comments
Shelah’s approachability ideal (part 1)
Given an infinite cardinal
Review: Is classical set theory compatible with quantum experiments?
Yesterday, I attended a talk at the Quantum Foundations seminar at the beautiful Perimeter Institute for Theoretical Physics (Waterloo, Ontario). The (somewhat provocative) title of the talk was “Is Classical Set Theory Compatible with Quantum Experiments?”, and the speaker was Radu … 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
Pure logic
While traveling downtown today, I came across a sign near a local church, with a quotation of Saint-Exupéry:
Jane’s Addiction visiting Toronto
Last night, I went to see a live show by Jane’s Addiction, in downtown Toronto. Here’s a video snippet from that show which I could found on YouTube: The playlist was excellent, but there was one song which I was … Continue reading
c.c.c. vs. the Knaster property
After my previous post on Mekler’s characterization of c.c.c. notions of forcing, Sam, Mike and myself discussed the value of it . We noticed that a prevalent verification of the c.c.c. goes like this: given an uncountable set of conditions, … Continue reading
Dushnik-Miller for regular cardinals (part 3)
Here is what we already know about the Dushnik-Miller theorem in the case of
A large cardinal in the constructible universe
In this post, we shall provide a proof of Silver’s theorem that the Erdos caridnal