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