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Nonspecial tree Luzin set Uniformly coherent Commutative projection system Countryman line super-Souslin tree reflection principles Foundations Ostaszewski square P-Ideal Dichotomy Constructible Universe Greatly Mahlo Chromatic number Successor of Regular Cardinal Universal Sequences Square-Brackets Partition Relations Almost Souslin Subtle cardinal PFA Knaster ZFC construction Microscopic Approach Parameterized proxy principle Small forcing Cardinal function Uniformization Distributive tree Erdos Cardinal strongly bounded groups Mandelbrot set countably metacompact Generalized descriptive set theory Rainbow sets Fast club Entangled linear order Iterated forcing b-scale Axiom R Amenable C-sequence diamond star L-space Ascent Path perfectly normal Selective Ultrafilter Hedetniemi's conjecture Baumgartner's square Well-behaved magma Strongly compact cardinal HOD PFA(S)[S] OCA Closed coloring tensor product graph Poset Singular cardinals combinatorics Successor of Singular Cardinal Local Club Condensation. Slim tree free Souslin tree Open Access regressive Souslin tree stationary hitting Rado's conjecture Cardinal Invariants polarized partition relation Partition relations for trees incompactness Absoluteness Almost-disjoint family Subadditive transformations Singular cofinality Singular Density SNR sap Large Cardinals specializable Souslin tree Non-saturation Ramsey theory over partitions Whitehead Problem stick Ineffable cardinal Dowker space C-sequence Cohen real Prikry-type forcing Sierpinski's onto mapping principle Intersection model weak Kurepa tree unbounded function Dushnik-Miller Forcing Chang's conjecture weak diamond Martin's Axiom Forcing with side conditions S-Space Subtle tree property Strongly Luzin set Fodor-type reflection Coherent tree Filter reflection Was Ulam right? square principles GMA Partition Relations club_AD Sakurai's Bell inequality O-space Interval topology on trees Precaliber coloring number stationary reflection Uniformly homogeneous Knaster and friends Shelah's Strong Hypothesis Hereditarily Lindelöf space Analytic sets ccc Strong coloring Lipschitz reduction Reduced Power Souslin Tree Ulam matrix positive partition relation Erdos-Hajnal graphs 54G20 Commutative cancellative semigroups approachability ideal Hindman's Theorem square weak square Diamond for trees Ascending path Prevalent singular cardinals middle diamond Subnormal ideal Diamond Club Guessing Vanishing levels Reflecting stationary set Monotonically far Antichain Minimal Walks Rock n' Roll Kurepa Hypothesis Fat stationary set full tree Sigma-Prikry Weakly compact cardinal Forcing Axioms free Boolean algebra projective Boolean algebra Aronszajn tree Almost countably chromatic Diamond-sharp xbox indecomposable filter Postprocessing function Jonsson cardinal Respecting tree AIM forcing Generalized Clubs very good scale nonmeager set higher Baire space
Tag Archives: Baumgartner’s square
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
A forcing axiom deciding the generalized Souslin Hypothesis
Joint work with Chris Lambie-Hanson. Abstract. We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal $\lambda$, … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E57, Baumgartner's square, Diamond, Forcing Axioms, Souslin Tree, square, super-Souslin tree
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