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super-Souslin tree Reduced Power club_AD Chromatic number C-sequence Distributive tree Foundations Parameterized proxy principle Minimal Walks Almost Souslin Constructible Universe P-Ideal Dichotomy Poset Uniformly homogeneous free Souslin tree Coherent tree Mandelbrot set Shelah's Strong Hypothesis Subtle tree property square principles Fodor-type reflection Prikry-type forcing Successor of Singular Cardinal stick Weakly compact cardinal incompactness Sakurai's Bell inequality weak square Ascent Path Amenable C-sequence Fast club Analytic sets Singular cofinality Knaster and friends Iterated forcing Erdos-Hajnal graphs Luzin set specializable Souslin tree Large Cardinals polarized partition relation Diamond for trees Slim tree reflection principles xbox PFA Filter reflection Selective Ultrafilter Reflecting stationary set O-space Ulam matrix positive partition relation Subtle cardinal unbounded function Strong coloring Dushnik-Miller Greatly Mahlo transformations Erdos Cardinal Open Access Cardinal Invariants Hindman's Theorem Square-Brackets Partition Relations Rado's conjecture OCA PFA(S)[S] Rock n' Roll Commutative cancellative semigroups Souslin Tree Microscopic Approach Dowker space full tree Cohen real Almost countably chromatic Subadditive coloring number Whitehead Problem Forcing Axioms Fat stationary set HOD Generalized Clubs Subnormal ideal ccc free Boolean algebra regressive Souslin tree Lipschitz reduction Diamond-sharp S-Space sap Kurepa Hypothesis Aronszajn tree Small forcing weak diamond very good scale stationary hitting Cardinal function AIM forcing Club Guessing Ramsey theory over partitions Jonsson cardinal approachability ideal Martin's Axiom Ostaszewski square Postprocessing function L-space Sigma-Prikry Rainbow sets SNR Singular cardinals combinatorics Well-behaved magma Antichain GMA Sierpinski's onto mapping principle higher Baire space Successor of Regular Cardinal indecomposable ultrafilter Nonspecial tree ZFC construction nonmeager set Almost-disjoint family Knaster countably metacompact Precaliber square Uniformly coherent Uniformization Prevalent singular cardinals Chang's conjecture Ineffable cardinal b-scale Singular Density Universal Sequences tensor product graph 54G20 stationary reflection Hedetniemi's conjecture Diamond Hereditarily Lindelöf space weak Kurepa tree Local Club Condensation. middle diamond Strongly Luzin set Was Ulam right Axiom R Non-saturation Generalized descriptive set theory strongly bounded groups Closed coloring Forcing diamond star Partition Relations Vanishing levels Absoluteness projective Boolean algebra
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Forcing with a Souslin tree makes $\mathfrak p=\omega_1$
I was meaning to include a proof of Farah’s lemma in my previous post, but then I realized that the slick proof assumes some background which may worth spelling out, first. Therefore, I am dedicating a short post for a … Continue reading
