Archives
Keywords
Monotonically far Strongly compact cardinal Open Access Erdos Cardinal sap Rado's conjecture Jonsson cardinal Subadditive Almost Souslin Hedetniemi's conjecture positive partition relation Weakly compact cardinal Selective Ultrafilter Successor of Regular Cardinal P-Ideal Dichotomy regressive Souslin tree Knaster Ineffable cardinal Dowker space weak diamond Commutative cancellative semigroups Forcing Axioms Analytic sets tensor product graph indecomposable filter S-Space Subnormal ideal OCA Filter reflection Souslin Tree O-space Shelah's Strong Hypothesis Ascent Path Reflecting stationary set incompactness Lipschitz reduction projective Boolean algebra very good scale Axiom R Cardinal function Hindman's Theorem Ostaszewski square ccc GMA Intersection model Mandelbrot set C-sequence Aronszajn tree Postprocessing function club_AD Knaster and friends b-scale PFA free Souslin tree Whitehead Problem Poset Small forcing Ramsey theory over partitions Prikry-type forcing middle diamond Singular cardinals combinatorics PFA(S)[S] Strong coloring Ulam matrix free Boolean algebra Subtle tree property Fast club reflection principles Distributive tree AIM forcing Martin's Axiom Forcing Singular cofinality Antichain Partition Relations Minimal Walks Local Club Condensation. Hereditarily Lindelöf space Strongly Luzin set unbounded function Diamond stationary hitting Nonspecial tree Universal Sequences Kurepa Hypothesis Foundations square principles Uniformly homogeneous square coloring number Uniformly coherent countably metacompact Commutative projection system Iterated forcing Successor of Singular Cardinal Countryman line Diamond-sharp weak square Non-saturation specializable Souslin tree super-Souslin tree stick Amenable C-sequence Sigma-Prikry strongly bounded groups stationary reflection Sierpinski's onto mapping principle full tree transformations Coherent tree HOD ZFC construction Luzin set Constructible Universe SNR approachability ideal Rock n' Roll Uniformization Chang's conjecture polarized partition relation higher Baire space Generalized Clubs Subtle cardinal weak Kurepa tree Club Guessing Almost-disjoint family Rainbow sets diamond star Almost countably chromatic L-space Microscopic Approach Prevalent singular cardinals xbox Cohen real Singular Density Was Ulam right? Closed coloring Square-Brackets Partition Relations Chromatic number 54G20 Sakurai's Bell inequality Fat stationary set Greatly Mahlo Slim tree nonmeager set Respecting tree Absoluteness Well-behaved magma Generalized descriptive set theory Dushnik-Miller Erdos-Hajnal graphs Precaliber Parameterized proxy principle Reduced Power Fodor-type reflection Entangled family Cardinal Invariants Diamond for trees Large Cardinals Vanishing levels
Category Archives: Blog
What’s next?
I took an offer for a tenure-track position at the Mathematics department of Bar-Ilan University.
Posted in Blog
13 Comments
Review: Stevo Todorcevic’s CRM-Fields-PIMS Prize Lecture
After winning the 2012 CRM-Fields-PIMS Prize, Stevo Todorcevic gave a series of talks on his research: at CRM, at PIMS and at the Fields Institute. The director of the Fields Institute asked me to write a short review on Stevo’s … Continue reading
Prikry Forcing
Recall that the chromatic number of a (symmetric) graph
Shelah’s approachability ideal (part 2)
In a previous post, we defined Shelah’s approachability ideal
Posted in Blog, Expository, Open Problems
Tagged approachability ideal, Club Guessing
Leave a comment
The uniformization property for
Given a subset of a regular uncountable cardinal
The uniformization property for
Given a subset of a regular uncountable cardinal
The Engelking-Karlowicz theorem, and a useful corollary
Theorem (Engelking-Karlowicz, 1965). For cardinals
Kurepa trees and ineffable cardinals
Recall that
Variations on diamond
Jensen’s diamond principle has many equivalent forms. The translation between these forms is often straight-forward, but there is one form whose equivalence to the usual form is somewhat surprising, and Devlin’s translation from one to the other, seems a little … Continue reading
The P-Ideal Dichotomy and the Souslin Hypothesis
John Krueger is visiting Toronto these days, and in a conversation today, we asked ourselves how do one prove the Abraham-Todorcevic theorem that PID implies SH. Namely, that the next statement implies that there are no Souslin trees: Definition. The … Continue reading
