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Constructible Universe O-space Prevalent singular cardinals stick Lipschitz reduction diamond star HOD Hedetniemi's conjecture Reflecting stationary set Sierpinski's onto mapping principle Entangled linear order Souslin Tree Almost Souslin Aronszajn tree Prikry-type forcing incompactness Foundations free Boolean algebra Nonspecial tree Countryman line weak Kurepa tree SNR approachability ideal Subtle cardinal Subadditive Distributive tree Hereditarily Lindelöf space Fodor-type reflection Sigma-Prikry transformations stationary hitting Non-saturation b-scale Successor of Regular Cardinal Ascent Path Respecting tree Uniformly homogeneous Uniformization Amenable C-sequence Singular cofinality stationary reflection Coherent tree Dowker space Monotonically far Knaster super-Souslin tree Ascending path projective Boolean algebra Poset Diamond-sharp Ineffable cardinal Closed coloring Martin's Axiom Vanishing levels Large Cardinals middle diamond Minimal Walks Selective Ultrafilter Hindman's Theorem Singular Density Iterated forcing Successor of Singular Cardinal L-space AIM forcing Strongly Luzin set perfectly normal Partition Relations Generalized Clubs higher Baire space specializable Souslin tree Reduced Power Subnormal ideal strongly bounded groups Mandelbrot set Cardinal Invariants Subtle tree property Ramsey theory over partitions PFA(S)[S] weak diamond Parameterized proxy principle Diamond for trees Forcing Axioms Was Ulam right? free Souslin tree Cardinal function Greatly Mahlo xbox polarized partition relation Almost-disjoint family tensor product graph C-sequence club_AD coloring number Analytic sets Local Club Condensation. 54G20 Interval topology on trees Singular cardinals combinatorics Strongly compact cardinal Square-Brackets Partition Relations unbounded function Postprocessing function ccc Knaster and friends ZFC construction countably metacompact Almost countably chromatic Generalized descriptive set theory Axiom R nonmeager set full tree Chromatic number Forcing Antichain Shelah's Strong Hypothesis PFA Kurepa Hypothesis OCA Erdos Cardinal Slim tree Rado's conjecture Luzin set Small forcing Weakly compact cardinal Fast club positive partition relation Ulam matrix very good scale Uniformly coherent Microscopic Approach Forcing with side conditions Commutative projection system Precaliber P-Ideal Dichotomy Partition relations for trees Well-behaved magma square Open Access Whitehead Problem Absoluteness Commutative cancellative semigroups Rock n' Roll square principles Club Guessing Intersection model Strong coloring indecomposable filter reflection principles Cohen real regressive Souslin tree Erdos-Hajnal graphs Jonsson cardinal Rainbow sets weak square Filter reflection sap Universal Sequences Dushnik-Miller Chang's conjecture Sakurai's Bell inequality Fat stationary set Diamond GMA S-Space Ostaszewski square
Tag Archives: Hereditarily Lindelöf space
The S-space problem, and the cardinal invariant $\mathfrak p$
Recall that an $S$-space is a regular hereditarily separable topological space which is not hereditarily Lindelöf. Do they exist? Consistently, yes. However, Szentmiklóssy proved that compact $S$-spaces do not exist, assuming Martin’s Axiom. Pushing this further, Todorcevic later proved that … Continue reading
Posted in Blog, Expository, Open Problems
Tagged Cardinal Invariants, Hereditarily Lindelöf space, P-Ideal Dichotomy, PFA(S)[S], S-Space
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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
Workshop on Set Theory and its Applications, February 2007
These are the slides of a talk given at the Workshop on Set Theory and its Applications workshop (Weizmann Institute, February 19, 2007). Talk Title: Nets of spaces having singular density Abstract: The weight of a topological space X is the … 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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