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S-Space Local Club Condensation. Fast club Closed coloring Precaliber Coherent tree middle diamond ZFC construction Large Cardinals Fat stationary set approachability ideal Strongly compact cardinal Postprocessing function Universal Sequences ccc transformations Forcing Axioms 54G20 Whitehead Problem Strongly Luzin set SNR Luzin set indecomposable ultrafilter Iterated forcing square Singular cardinals combinatorics stick countably metacompact Sierpinski's onto mapping principle Rainbow sets Ramsey theory over partitions Almost countably chromatic Uniformly coherent Microscopic Approach AIM forcing Commutative cancellative semigroups Cardinal Invariants Minimal Walks Kurepa Hypothesis Commutative projection system Foundations Greatly Mahlo Axiom R Club Guessing P-Ideal Dichotomy Ostaszewski square reflection principles full tree higher Baire space Diamond Ascent Path Well-behaved magma Rado's conjecture club_AD Sakurai's Bell inequality Generalized Clubs Prikry-type forcing Chromatic number Hedetniemi's conjecture positive partition relation diamond star Distributive tree unbounded function Forcing specializable Souslin tree Square-Brackets Partition Relations free Souslin tree Generalized descriptive set theory Lipschitz reduction Parameterized proxy principle Jonsson cardinal Mandelbrot set coloring number Absoluteness nonmeager set xbox Was Ulam right Filter reflection Small forcing PFA Intersection model Almost-disjoint family Amenable C-sequence Slim tree Countryman line Hereditarily Lindelöf space Poset Successor of Regular Cardinal stationary hitting Erdos Cardinal weak square Cohen real square principles strongly bounded groups sap OCA C-sequence weak diamond PFA(S)[S] Dowker space Constructible Universe Nonspecial tree Almost Souslin stationary reflection Dushnik-Miller Knaster Erdos-Hajnal graphs Shelah's Strong Hypothesis Reduced Power Singular cofinality Analytic sets Chang's conjecture incompactness Singular Density HOD Open Access Aronszajn tree Respecting tree regressive Souslin tree Rock n' Roll projective Boolean algebra Fodor-type reflection Prevalent singular cardinals Partition Relations super-Souslin tree very good scale Subtle tree property Ineffable cardinal Diamond-sharp Diamond for trees Strong coloring Knaster and friends weak Kurepa tree Antichain Weakly compact cardinal b-scale Cardinal function Uniformization Martin's Axiom Reflecting stationary set Subnormal ideal Subadditive GMA Successor of Singular Cardinal Souslin Tree Subtle cardinal Non-saturation Ulam matrix Vanishing levels Hindman's Theorem tensor product graph L-space free Boolean algebra Sigma-Prikry Uniformly homogeneous Selective Ultrafilter polarized partition relation O-space
Tag Archives: b-scale
6th European Set Theory Conference, July 2017
I gave a 3-lecture tutorial at the 6th European Set Theory Conference in Budapest, July 2017. Title: Strong colorings and their applications. Abstract. Consider the following questions. Is the product of two $\kappa$-cc partial orders again $\kappa$-cc? Does there exist … Continue reading
Posted in Invited Talks, Open Problems
Tagged b-scale, Cohen real, Luzin set, Minimal Walks, Souslin Tree, Square-Brackets Partition Relations
4 Comments
Open coloring and the cardinal invariant $\mathfrak b$
Nik Weaver asked for a direct proof of the fact that Todorcevic’s axiom implies the failure of CH fails. Here goes. Notation. For a set $X$, we write $[X]^2$ for the set of unordered pairs $\{ \{x,x’\}\mid x,x’\in X, x\neq … Continue reading
The S-space problem, and the cardinal invariant $\mathfrak b$
Recall that an S-space is a regular hereditarily separable topological space which is not hereditarily Lindelöf. In a previous post, we showed that such a space exists after adding a Cohen real. Here, we shall construct one from an arithmetic … Continue reading
The S-space problem, and the cardinal invariant $\mathfrak b$
Recall that an S-space is a regular hereditarily separable topological space which is not hereditarily Lindelöf. In a previous post, we showed that such a space exists after adding a Cohen real. Here, we shall construct one from an arithmetic … 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 2)
In this post, we shall provide a proof of Todorcevic’s theorem, that $\mathfrak b=\omega_1$ implies $\omega_1\not\rightarrow(\omega_1,\omega+2)^2$. This will show that the Erdos-Rado theorem that we discussed in an earlier post, is consistently optimal. Our exposition of Todorcevic’s theorem would be … Continue reading
Posted in Blog, Expository
Tagged b-scale, Dushnik-Miller, Partition Relations, Square-Brackets Partition Relations
5 Comments
Infinite Combinatorial Topology
Back in 2005, as a master student, I attended a course by Boaz Tsaban, entitled “Infinite Combinatorial Topology”. A friend and I decided to produce lecture notes, but in a somewhat loose sense, that is: we sometimes omit material given … Continue reading
Posted in Notes
Tagged b-scale, Cardinal function, Cardinal Invariants, Hereditarily Lindelöf space
8 Comments
