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AIM forcing reflection principles Amenable C-sequence Almost Souslin Mandelbrot set Uniformly coherent Ineffable cardinal Coherent tree Hedetniemi's conjecture PFA Successor of Regular Cardinal Constructible Universe Generalized Clubs Closed coloring Weakly compact cardinal Universal Sequences stationary reflection Square-Brackets Partition Relations Hereditarily Lindelöf space positive partition relation Parameterized proxy principle Club Guessing square principles countably metacompact transformations weak diamond Nonspecial tree O-space Rainbow sets Sierpinski's onto mapping principle Uniformization Whitehead Problem Was Ulam right Slim tree Axiom R Diamond super-Souslin tree coloring number Sakurai's Bell inequality Cohen real Reduced Power Commutative cancellative semigroups PFA(S)[S] stationary hitting Singular cardinals combinatorics Almost countably chromatic HOD Forcing Axioms Almost-disjoint family Martin's Axiom Ulam matrix Diamond for trees middle diamond weak square Analytic sets Generalized descriptive set theory Partition Relations incompactness Prevalent singular cardinals Dushnik-Miller b-scale free Souslin tree nonmeager set Cardinal Invariants Ascent Path Chang's conjecture C-sequence Chromatic number Greatly Mahlo Souslin Tree Singular Density approachability ideal SNR ccc Open Access S-Space Selective Ultrafilter Uniformly homogeneous Fast club Antichain stick Microscopic Approach specializable Souslin tree Non-saturation Minimal Walks tensor product graph Kurepa Hypothesis Erdos-Hajnal graphs indecomposable ultrafilter Ostaszewski square Foundations higher Baire space Knaster Strong coloring Diamond-sharp Erdos Cardinal Forcing Distributive tree regressive Souslin tree L-space Luzin set unbounded function diamond star club_AD Fodor-type reflection Ramsey theory over partitions Postprocessing function GMA Knaster and friends Jonsson cardinal full tree Lipschitz reduction Subtle cardinal Hindman's Theorem strongly bounded groups Absoluteness Poset Rado's conjecture Rock n' Roll Dowker space weak Kurepa tree Well-behaved magma Subtle tree property Reflecting stationary set Small forcing Shelah's Strong Hypothesis Vanishing levels very good scale OCA square free Boolean algebra xbox sap Iterated forcing Cardinal function Sigma-Prikry Singular cofinality Prikry-type forcing Large Cardinals Successor of Singular Cardinal P-Ideal Dichotomy ZFC construction Strongly Luzin set Fat stationary set Filter reflection projective Boolean algebra Local Club Condensation. Subnormal ideal Precaliber Subadditive Aronszajn tree polarized partition relation 54G20
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An $S$-space from a Cohen real
Recall that an $S$-space is a regular hereditarily separable topological space which is not hereditarily Lindelöf. In this post, we shall establish the consistency of the existence of such a space. Theorem (Roitman, 1979). Let $\mathbb C=({}^{<\omega}\omega,\subseteq)$ be the notion of … Continue reading
