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### 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

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

# 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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