### Archives

### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

Forcing PFA(S)[S] Prikry-type forcing Large Cardinals Ascent Path 20M14 Singular Density L-space Forcing Axioms Hindman's Theorem Slim tree Axiom R ccc Hereditarily Lindelöf space Cardinal function Distributive tree polarized partition relation very good scale Rock n' Roll Commutative cancellative semigroups 05A17 Universal Sequences Constructible Universe Erdos-Hajnal graphs Square-Brackets Partition Relations Dushnik-Miller coloring number Rado's conjecture square Cohen real Successor of Singular Cardinal tensor product graph Non-saturation weak diamond projective Boolean algebra Cardinal Invariants Rainbow sets Reduced Power Almost Souslin incompactness Generalized Clubs Uniformly coherent Absoluteness Shelah's Strong Hypothesis Whitehead Problem Antichain free Boolean algebra Weakly compact cardinal Partition Relations Singular cardinals combinatorics Souslin Tree Ostaszewski square Successor of Regular Cardinal b-scale Kurepa Hypothesis Almost countably chromatic Fat stationary set Coherent tree stationary reflection Martin's Axiom square principles stationary hitting Microscopic Approach Hedetniemi's conjecture PFA 05D10 Stevo Todorcevic reflection principles Uniformization Poset P-Ideal Dichotomy Nonspecial tree Selective Ultrafilter Minimal Walks Small forcing Prevalent singular cardinals 11P99 xbox Jonsson cardinal approachability ideal OCA sap Postprocessing function Almost-disjoint famiy Knaster Club Guessing Foundations Mandelbrot set weak square Chromatic number Parameterized proxy principle Singular coﬁnality middle diamond Sakurai's Bell inequality Erdos Cardinal Aronszajn tree Fodor-type reflection HOD diamond star Diamond Chang's conjecture S-Space Fast club

# Category Archives: Topology

## 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

## A topological reflection principle equivalent to Shelah’s strong hypothesis

Abstract: We notice that Shelah’s Strong Hypothesis (SSH) is equivalent to the following reflection principle: Suppose $\mathbb X$ is an (infinite) first-countable space whose density is a regular cardinal, $\kappa$. If every separable subspace of $\mathbb X$ is of cardinality at most … Continue reading

Posted in Compactness, Publications, Topology
Tagged 03E04, 03E65, 54G15, Shelah's Strong Hypothesis
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