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### Keywords

PFA(S)[S] Forcing Dushnik-Miller polarized partition relation Successor of Regular Cardinal S-Space Erdos Cardinal Cohen real Antichain square b-scale Knaster Partition Relations Cardinal Invariants incompactness Hedetniemi's conjecture Foundations Rado's conjecture Jonsson cardinal Prevalent singular cardinals OCA very good scale Commutative cancellative semigroups HOD Almost-disjoint famiy L-space middle diamond Club Guessing Small forcing Selective Ultrafilter Martin's Axiom Souslin Tree Almost Souslin P-Ideal Dichotomy coloring number Singular Density Minimal Walks Weakly compact cardinal Aronszajn tree Diamond diamond star Fodor-type reflection sap 05A17 Slim tree Sakurai's Bell inequality Prikry-type forcing xbox Almost countably chromatic reflection principles Chromatic number Constructible Universe Singular cardinals combinatorics Poset Coherent tree Generalized Clubs Universal Sequences Rainbow sets Singular Cofinality Rock n' Roll Non-saturation Hereditarily Lindelöf space 20M14 stationary reflection Hindman's Theorem Successor of Singular Cardinal Ascent Path Large Cardinals Square-Brackets Partition Relations Chang's conjecture projective Boolean algebra free Boolean algebra Forcing Axioms Microscopic Approach 05D10 Uniformization Erdos-Hajnal graphs tensor product graph Mandelbrot set weak square Whitehead Problem weak diamond Absoluteness Reduced Power Axiom R Fat stationary set Kurepa Hypothesis Fast club Stevo Todorcevic PFA Shelah's Strong Hypothesis Ostaszewski square stationary hitting approachability ideal Singular coﬁnality Parameterized proxy principle Cardinal function 11P99 ccc

# Tag Archives: 54G15

## 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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