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Large Cardinals Cardinal Invariants polarized partition relation Iterated forcing b-scale Subtle tree property PFA approachability ideal stick Selective Ultrafilter Prikry-type forcing Antichain countably metacompact Fast club Was Ulam right? Hindman's Theorem HOD Cardinal function Luzin set weak Kurepa tree square Uniformly coherent Rock n' Roll Dushnik-Miller Fat stationary set Countryman line Erdos Cardinal Rainbow sets Ostaszewski square Ramsey theory over partitions Forcing Axioms transformations Almost Souslin Generalized descriptive set theory stationary hitting Hedetniemi's conjecture Generalized Clubs Vanishing levels Lipschitz reduction Parameterized proxy principle C-sequence higher Baire space Entangled linear order Open Access specializable Souslin tree Local Club Condensation. ccc Successor of Singular Cardinal Commutative cancellative semigroups Precaliber Prevalent singular cardinals Closed coloring Strongly Luzin set Aronszajn tree Nonspecial tree Chromatic number Subnormal ideal P-Ideal Dichotomy Diamond-sharp Singular cardinals combinatorics Singular cofinality Shelah's Strong Hypothesis 54G20 Postprocessing function Successor of Regular Cardinal super-Souslin tree Analytic sets Uniformly homogeneous Sierpinski's onto mapping principle L-space positive partition relation Whitehead Problem Forcing weak diamond Non-saturation Amenable C-sequence ZFC construction Rado's conjecture Ascent Path Singular Density projective Boolean algebra Jonsson cardinal Almost countably chromatic Forcing with side conditions reflection principles SNR Chang's conjecture Subadditive Absoluteness PFA(S)[S] Constructible Universe free Boolean algebra weak square Ulam matrix sap Intersection model free Souslin tree S-Space club_AD O-space Filter reflection Partition relations for trees xbox Strongly compact cardinal Diamond full tree GMA Coherent tree Sigma-Prikry Knaster and friends Weakly compact cardinal Ascending path Small forcing Partition Relations Club Guessing indecomposable filter Monotonically far OCA unbounded function Erdos-Hajnal graphs Diamond for trees Almost-disjoint family Universal Sequences incompactness Commutative projection system Strong coloring AIM forcing stationary reflection Axiom R Interval topology on trees Martin's Axiom Sakurai's Bell inequality nonmeager set regressive Souslin tree Uniformization Greatly Mahlo Mandelbrot set Fodor-type reflection strongly bounded groups Microscopic Approach Well-behaved magma Dowker space Respecting tree Hereditarily Lindelöf space tensor product graph Distributive tree Reduced Power Knaster coloring number Kurepa Hypothesis very good scale Poset Minimal Walks Reflecting stationary set Square-Brackets Partition Relations square principles diamond star perfectly normal middle diamond Cohen real Slim tree Foundations Souslin Tree Subtle cardinal Ineffable cardinal
Tag Archives: Cardinal function
On topological spaces of singular density and minimal weight
Abstract: We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the Prevalent Singular cardinals Hypothesis (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf. The assumption … 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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