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