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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

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

# 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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