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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
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### Keywords

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