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square principles Distributive tree unbounded function Amenable C-sequence Sigma-Prikry Chang's conjecture Constructible Universe Subtle tree property Filter reflection Diamond Martin's Axiom 54G20 PFA(S)[S] Intersection model diamond star Precaliber free Souslin tree Subnormal ideal Fat stationary set Vanishing levels tensor product graph Knaster sap incompactness higher Baire space full tree super-Souslin tree Prikry-type forcing Was Ulam right Analytic sets Coherent tree Iterated forcing Singular cardinals combinatorics Greatly Mahlo Erdos Cardinal Luzin set weak square PFA Ramsey theory over partitions b-scale Chromatic number P-Ideal Dichotomy OCA Uniformly coherent Successor of Regular Cardinal Open Access Hereditarily Lindelöf space Subadditive Whitehead Problem Parameterized proxy principle Minimal Walks transformations SNR xbox Reduced Power Nonspecial tree C-sequence stationary hitting Forcing Axioms Non-saturation Antichain Poset Commutative cancellative semigroups Rock n' Roll Fast club Souslin Tree weak diamond regressive Souslin tree middle diamond countably metacompact Sakurai's Bell inequality very good scale Microscopic Approach Postprocessing function specializable Souslin tree Singular Density L-space Universal Sequences S-Space Countryman line Jonsson cardinal Diamond-sharp square Generalized Clubs Rainbow sets polarized partition relation Club Guessing Strongly compact cardinal Successor of Singular Cardinal Strong coloring Cardinal function free Boolean algebra Cohen real Rado's conjecture Uniformly homogeneous Subtle cardinal Large Cardinals Ineffable cardinal Respecting tree HOD Knaster and friends Forcing club_AD Reflecting stationary set Slim tree stick Ulam matrix Generalized descriptive set theory Closed coloring Erdos-Hajnal graphs Commutative projection system stationary reflection Prevalent singular cardinals approachability ideal Strongly Luzin set reflection principles GMA Almost-disjoint family strongly bounded groups Partition Relations nonmeager set Local Club Condensation. Cardinal Invariants Aronszajn tree Foundations Diamond for trees ccc Absoluteness ZFC construction Small forcing indecomposable ultrafilter Almost Souslin weak Kurepa tree Dushnik-Miller AIM forcing Square-Brackets Partition Relations Shelah's Strong Hypothesis Uniformization Kurepa Hypothesis Dowker space Weakly compact cardinal Well-behaved magma Singular cofinality Fodor-type reflection positive partition relation Ostaszewski square projective Boolean algebra Hedetniemi's conjecture coloring number Axiom R Almost countably chromatic Hindman's Theorem Selective Ultrafilter Lipschitz reduction Sierpinski's onto mapping principle O-space Mandelbrot set Ascent Path
Tag Archives: Cardinal Invariants
On the ideal J[kappa]
Abstract. Motivated by a question from a recent paper by Gilton, Levine and Stejskalova, we obtain a new characterization of the ideal $J[\kappa]$, from which we confirm that $\kappa$-Souslin trees exist in various models of interest. As a corollary we … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged Cardinal Invariants, Cohen real, nonmeager set
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Bell’s theorem on the cardinal invariant $\mathfrak p$
In this post, we shall provide a proof to a famous theorem of Murray Bell stating that $MA_\kappa(\text{the class of }\sigma\text{-centered posets})$ holds iff $\kappa<\mathfrak p$. We commence with defining the cardinal invariant $\mathfrak p$. For sets $A$ and $B$, … Continue reading
Bell’s theorem on the cardinal invariant $\mathfrak p$
In this post, we shall provide a proof to a famous theorem of Murray Bell stating that $MA_\kappa(\text{the class of }\sigma\text{-centered posets})$ holds iff $\kappa<\mathfrak p$. We commence with defining the cardinal invariant $\mathfrak p$. For sets $A$ and $B$, … 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
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