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