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- 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

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

# 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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