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