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countably metacompact Mandelbrot set Ramsey theory over partitions free Souslin tree AIM forcing Successor of Singular Cardinal Fodor-type reflection Microscopic Approach stationary hitting club_AD Universal Sequences specializable Souslin tree Local Club Condensation. weak Kurepa tree approachability ideal Respecting tree Jonsson cardinal Cardinal function Shelah's Strong Hypothesis Singular cardinals combinatorics Ineffable cardinal Subtle tree property regressive Souslin tree Whitehead Problem Hedetniemi's conjecture Forcing Axioms Distributive tree Small forcing Chang's conjecture Erdos-Hajnal graphs PFA(S)[S] weak diamond Minimal Walks Martin's Axiom Intersection model Club Guessing 54G20 Rock n' Roll Knaster and friends Subtle cardinal Singular Density Cohen real Slim tree Diamond Sigma-Prikry Strongly Luzin set projective Boolean algebra super-Souslin tree Subnormal ideal P-Ideal Dichotomy Closed coloring Luzin set diamond star Reflecting stationary set Lipschitz reduction full tree Analytic sets Subadditive Foundations Generalized descriptive set theory Open Access b-scale xbox Amenable C-sequence strongly bounded groups Prikry-type forcing stationary reflection positive partition relation Almost countably chromatic Reduced Power Diamond-sharp Erdos Cardinal higher Baire space Precaliber Absoluteness Large Cardinals Axiom R O-space Poset GMA C-sequence Nonspecial tree HOD Ostaszewski square Strong coloring Dushnik-Miller Parameterized proxy principle nonmeager set transformations Constructible Universe Uniformization Uniformly coherent Square-Brackets Partition Relations middle diamond Rainbow sets free Boolean algebra Non-saturation Knaster Fat stationary set Commutative cancellative semigroups Strongly compact cardinal Ascent Path Almost Souslin incompactness reflection principles Kurepa Hypothesis Partition Relations Souslin Tree Aronszajn tree Chromatic number ZFC construction very good scale Diamond for trees SNR Filter reflection weak square Almost-disjoint family unbounded function Iterated forcing Hereditarily Lindelöf space stick Postprocessing function tensor product graph Prevalent singular cardinals S-Space Generalized Clubs ccc Countryman line Antichain Rado's conjecture sap Weakly compact cardinal OCA polarized partition relation square principles Selective Ultrafilter Uniformly homogeneous Sierpinski's onto mapping principle Cardinal Invariants Successor of Regular Cardinal Was Ulam right? Greatly Mahlo Commutative projection system Singular cofinality square Hindman's Theorem Sakurai's Bell inequality Ulam matrix Forcing indecomposable filter coloring number Dowker space Coherent tree Vanishing levels Well-behaved magma PFA Fast club L-space
Category Archives: Blog
Forcing with a Souslin tree makes
I was meaning to include a proof of Farah’s lemma in my previous post, but then I realized that the slick proof assumes some background which may worth spelling out, first. Therefore, I am dedicating a short post for a … Continue reading
Forcing with a Souslin tree makes
I was meaning to include a proof of Farah’s lemma in my previous post, but then I realized that the slick proof assumes some background which may worth spelling out, first. Therefore, I am dedicating a short post for a … Continue reading
The S-space problem, and the cardinal invariant
Recall that an
Posted in Blog, Expository, Open Problems
Tagged Hereditarily Lindelöf space, P-Ideal Dichotomy, PFA(S)[S], S-Space
4 Comments
Jones’ theorem on the cardinal invariant
This post continues the study of the cardinal invariant
Jones’ theorem on the cardinal invariant
This post continues the study of the cardinal invariant
Posted in Blog, Expository
Tagged polarized partition relation, Sierpinski's onto mapping principle
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Erdős 100
The influential mathematician Paul Erdős was born 100 years ago, 26 March 1913, in Budapest. One evidence of his impact on mathematics is reflected in the particular list of invited speakers for the upcoming conference in his honor. Erdős is also … Continue reading
Bell’s theorem on the cardinal invariant
In this post, we shall provide a proof to a famous theorem of Murray Bell stating that
Bell’s theorem on the cardinal invariant
In this post, we shall provide a proof to a famous theorem of Murray Bell stating that
The
Here is an elementary proof of (the finitary version of) the
Posted in Blog, Expository, Surprisingly short
17 Comments
A natural Mandelbrot set
Chris Hadfield is a Canadian astronaut, with a very high-profile twitter account. He posts there beautiful photos everyday, and I (plus half a million followers) enjoy it very much. Today, Chris posted the following picture: and I find it quite … Continue reading
