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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
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### Keywords

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

# 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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