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- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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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