Archives
Keywords
Foundations reflection principles stationary hitting Open Access nonmeager set Analytic sets Almost-disjoint family approachability ideal Mandelbrot set Nonspecial tree PFA Large Cardinals coloring number Dowker space 54G20 Shelah's Strong Hypothesis Forcing Axioms Diamond Monotonically far perfectly normal Souslin Tree transformations Forcing with side conditions Singular cardinals combinatorics Selective Ultrafilter Rado's conjecture Interval topology on trees Partition Relations Commutative projection system Whitehead Problem Intersection model Aronszajn tree Was Ulam right? S-Space Luzin set Non-saturation Knaster and friends Precaliber L-space free Boolean algebra Generalized Clubs Dushnik-Miller Singular Density Respecting tree positive partition relation Filter reflection Hereditarily Lindelöf space weak diamond sap Fat stationary set Ineffable cardinal Forcing Subtle tree property Almost Souslin Parameterized proxy principle xbox Hedetniemi's conjecture Ostaszewski square middle diamond Minimal Walks Strong coloring PFA(S)[S] Chang's conjecture Ulam matrix stationary reflection indecomposable filter Subadditive Kurepa Hypothesis HOD Jonsson cardinal Sigma-Prikry Martin's Axiom SNR Ascent Path Distributive tree GMA Diamond for trees Almost countably chromatic projective Boolean algebra square principles Chromatic number tensor product graph Weakly compact cardinal Greatly Mahlo Successor of Singular Cardinal b-scale Strongly Luzin set Reduced Power Countryman line Uniformly homogeneous Subtle cardinal Erdos-Hajnal graphs Ascending path Entangled linear order Sakurai's Bell inequality Diamond-sharp P-Ideal Dichotomy free Souslin tree Successor of Regular Cardinal full tree strongly bounded groups AIM forcing C-sequence very good scale Postprocessing function specializable Souslin tree club_AD Local Club Condensation. polarized partition relation countably metacompact Closed coloring incompactness Partition relations for trees regressive Souslin tree square Generalized descriptive set theory weak square Erdos Cardinal Sierpinski's onto mapping principle Club Guessing Prikry-type forcing Strongly compact cardinal Cardinal function Knaster ZFC construction Microscopic Approach Vanishing levels Uniformly coherent Ramsey theory over partitions Prevalent singular cardinals ccc Constructible Universe Subnormal ideal Coherent tree Cohen real Axiom R higher Baire space Absoluteness Well-behaved magma Rainbow sets super-Souslin tree weak Kurepa tree OCA Reflecting stationary set Poset Singular cofinality unbounded function Fast club Antichain Lipschitz reduction Uniformization Universal Sequences stick Cardinal Invariants Hindman's Theorem Commutative cancellative semigroups Slim tree Fodor-type reflection Square-Brackets Partition Relations diamond star Amenable C-sequence O-space Iterated forcing Small forcing Rock n' Roll
Tag Archives: Fast club
Prikry forcing may add a Souslin tree
A celebrated theorem of Shelah states that adding a Cohen real introduces a Souslin tree. Are there any other examples of notions of forcing that add a $\kappa$-Souslin tree? and why is this of interest? My motivation comes from a … Continue reading