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tensor product graph Subtle cardinal Monotonically far Lipschitz reduction polarized partition relation Ramsey theory over partitions Baumgartner's square SNR Minimal Walks Chang's conjecture Successor of Regular Cardinal Aronszajn tree Knaster Uniformization Selective Ultrafilter weak Kurepa tree OCA Martin's Axiom P-Ideal Dichotomy Prevalent singular cardinals Uniformly homogeneous Respecting tree HOD Jonsson cardinal Foundations nonmeager set Non-saturation incompactness diamond star stationary reflection Interval topology on trees transformations Hereditarily Lindelöf space Diamond-sharp Greatly Mahlo Dushnik-Miller Cardinal function Singular cofinality Weakly compact cardinal Cardinal Invariants Square-Brackets Partition Relations full tree Forcing Distributive tree Dowker space Poset Prikry-type forcing Nonspecial tree Hedetniemi's conjecture Successor of Singular Cardinal Constructible Universe b-scale Precaliber Open Access L-space Whitehead Problem indecomposable filter middle diamond positive partition relation Chromatic number strongly bounded groups Small forcing approachability ideal Absoluteness Rainbow sets Amenable C-sequence Rado's conjecture stick Sierpinski's onto mapping principle Entangled linear order square weak diamond projective Boolean algebra Ulam matrix Cohen real Uniformly coherent Forcing with side conditions Diamond AIM forcing Microscopic Approach very good scale Singular cardinals combinatorics Axiom R Closed coloring regressive Souslin tree Sakurai's Bell inequality Ascent Path Slim tree ccc Commutative projection system C-sequence Ineffable cardinal Partition Relations unbounded function 54G20 Vanishing levels Iterated forcing Almost countably chromatic Filter reflection PFA weak square Parameterized proxy principle Reduced Power free Souslin tree perfectly normal Was Ulam right? Singular Density Strong coloring Partition relations for trees Antichain Postprocessing function Universal Sequences Sigma-Prikry GMA Ostaszewski square higher Baire space Rock n' Roll Coherent tree S-Space Strongly Luzin set Countryman line Intersection model Commutative cancellative semigroups Subnormal ideal Almost-disjoint family Hindman's Theorem Subtle tree property Erdos-Hajnal graphs O-space Erdos Cardinal Shelah's Strong Hypothesis Well-behaved magma ZFC construction Luzin set Analytic sets Fat stationary set Club Guessing reflection principles stationary hitting Forcing Axioms Local Club Condensation. Large Cardinals sap Souslin Tree Fodor-type reflection Diamond for trees Strongly compact cardinal Almost Souslin Subadditive xbox Reflecting stationary set Generalized Clubs free Boolean algebra club_AD PFA(S)[S] Generalized descriptive set theory Kurepa Hypothesis Ascending path Knaster and friends coloring number super-Souslin tree Mandelbrot set specializable Souslin tree countably metacompact Fast club square principles
Tag Archives: full tree
More notions of forcing add a square
Joint work with Yair Hayut and Zhixing You. Abstract. Foreman and Magidor showed that the continuum hypothesis implies the existence of a countably-closed $\aleph_2$-cc forcing notion $\mathbb P$ for adding $\square_{\omega_1}$. Here, we show that $\mathbb P$ may consistently be … Continue reading
Posted in Squares and Diamonds
Tagged Baumgartner's square, full tree, Souslin Tree, square principles, super-Souslin tree
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Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A $\kappa$-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading
