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