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