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weak diamond Constructible Universe Well-behaved magma incompactness Subtle cardinal Foundations perfectly normal Commutative projection system Ulam matrix Local Club Condensation. Microscopic Approach Minimal Walks ZFC construction Successor of Singular Cardinal Kurepa Hypothesis Greatly Mahlo Whitehead Problem sap Cohen real Knaster Vanishing levels countably metacompact Subnormal ideal xbox Uniformization L-space regressive Souslin tree Diamond-sharp Poset club_AD Souslin Tree Knaster and friends middle diamond Cardinal function Successor of Regular Cardinal Reflecting stationary set ccc tensor product graph square HOD Luzin set Was Ulam right? stationary hitting Sierpinski's onto mapping principle Aronszajn tree Singular cofinality AIM forcing Precaliber Rock n' Roll GMA Interval topology on trees Commutative cancellative semigroups OCA polarized partition relation Mandelbrot set Parameterized proxy principle Postprocessing function Fast club Fodor-type reflection Sigma-Prikry Prevalent singular cardinals Distributive tree Ineffable cardinal Singular Density Rado's conjecture Forcing Axioms Weakly compact cardinal Non-saturation Small forcing unbounded function approachability ideal Erdos-Hajnal graphs Almost Souslin Ascending path C-sequence Jonsson cardinal Erdos Cardinal Respecting tree PFA Partition relations for trees square principles Ostaszewski square Intersection model Diamond Diamond for trees free Souslin tree Strongly compact cardinal very good scale nonmeager set Generalized Clubs Sakurai's Bell inequality stationary reflection Dushnik-Miller b-scale Strong coloring Forcing with side conditions positive partition relation Chromatic number Subtle tree property full tree PFA(S)[S] Countryman line Square-Brackets Partition Relations Slim tree indecomposable filter 54G20 Coherent tree Chang's conjecture specializable Souslin tree Forcing projective Boolean algebra Entangled linear order Partition Relations Dowker space super-Souslin tree weak square Shelah's Strong Hypothesis Prikry-type forcing Lipschitz reduction SNR Absoluteness free Boolean algebra Monotonically far O-space Rainbow sets Club Guessing diamond star Subadditive Hindman's Theorem Iterated forcing Axiom R P-Ideal Dichotomy Closed coloring higher Baire space Universal Sequences Large Cardinals reflection principles Hereditarily Lindelöf space transformations Uniformly coherent Filter reflection weak Kurepa tree Selective Ultrafilter Open Access Hedetniemi's conjecture coloring number Almost-disjoint family Amenable C-sequence Nonspecial tree Analytic sets strongly bounded groups Fat stationary set Uniformly homogeneous Singular cardinals combinatorics Ascent Path Reduced Power Almost countably chromatic Ramsey theory over partitions S-Space Strongly Luzin set Antichain Cardinal Invariants stick Martin's Axiom Generalized descriptive set theory
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
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
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
