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middle diamond Intersection model Antichain ccc Respecting tree Analytic sets Uniformization free Souslin tree Generalized descriptive set theory Non-saturation stationary hitting square Club Guessing Countryman line Erdos-Hajnal graphs P-Ideal Dichotomy regressive Souslin tree Poset Partition relations for trees Martin's Axiom Small forcing GMA Fodor-type reflection reflection principles Subadditive Minimal Walks xbox Ascending path O-space Parameterized proxy principle Ulam matrix Forcing with side conditions Chang's conjecture 54G20 Hedetniemi's conjecture Diamond-sharp indecomposable filter Reflecting stationary set SNR Mandelbrot set Subtle cardinal Ostaszewski square Knaster Diamond Absoluteness Distributive tree Subnormal ideal Cardinal function Prevalent singular cardinals Rock n' Roll incompactness Successor of Singular Cardinal Axiom R Monotonically far Erdos Cardinal Luzin set PFA Hereditarily Lindelöf space Rado's conjecture polarized partition relation Coherent tree club_AD Square-Brackets Partition Relations Weakly compact cardinal Interval topology on trees stick Constructible Universe Lipschitz reduction Greatly Mahlo Iterated forcing Commutative projection system projective Boolean algebra Local Club Condensation. AIM forcing diamond star Selective Ultrafilter Chromatic number Strong coloring Well-behaved magma Jonsson cardinal Generalized Clubs Fast club Diamond for trees Dushnik-Miller tensor product graph positive partition relation Strongly Luzin set Partition Relations square principles weak Kurepa tree Whitehead Problem S-Space approachability ideal Almost countably chromatic Hindman's Theorem Forcing sap L-space C-sequence weak square OCA Strongly compact cardinal Slim tree b-scale Souslin Tree Kurepa Hypothesis Ineffable cardinal unbounded function Sakurai's Bell inequality full tree higher Baire space Sierpinski's onto mapping principle Reduced Power Uniformly coherent Uniformly homogeneous Singular Density Aronszajn tree specializable Souslin tree Prikry-type forcing Postprocessing function Precaliber nonmeager set Nonspecial tree ZFC construction Open Access Ascent Path HOD Fat stationary set strongly bounded groups Rainbow sets super-Souslin tree Universal Sequences weak diamond perfectly normal Microscopic Approach Singular cardinals combinatorics Forcing Axioms very good scale Filter reflection free Boolean algebra Dowker space Cardinal Invariants Subtle tree property Amenable C-sequence Almost Souslin Successor of Regular Cardinal Shelah's Strong Hypothesis Ramsey theory over partitions Knaster and friends Was Ulam right? Entangled linear order Commutative cancellative semigroups PFA(S)[S] stationary reflection Almost-disjoint family countably metacompact Singular cofinality Closed coloring Cohen real transformations coloring number Foundations Sigma-Prikry Vanishing levels Large Cardinals
Tag Archives: Microscopic Approach
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 microscopic approach to Souslin-tree constructions. Part II
Joint work with Ari Meir Brodsky. Abstract. In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known $\diamondsuit$-based constructions of Souslin trees with various additional properties may be rendered as applications of … Continue reading
A remark on Schimmerling’s question
Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading
A microscopic approach to Souslin-tree constructions. Part I
Joint work with Ari Meir Brodsky. Abstract. We propose a parameterized proxy principle from which $\kappa$-Souslin trees with various additional features can be constructed, regardless of the identity of $\kappa$. We then introduce the microscopic approach, which is a simple … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E65, 05C05, Coherent tree, Diamond, Microscopic Approach, Parameterized proxy principle, Slim tree, Souslin Tree, square, xbox
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Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading
Forcing and its Applications Retrospective Workshop, April 2015
I gave an invited talk at Forcing and its Applications Retrospective Workshop, Toronto, April 1st, 2015. Title: A microscopic approach to Souslin trees constructions Abstract: We present an approach to construct $\kappa$-Souslin trees that is insensitive to the identity of … Continue reading
Posted in Invited Talks
Tagged Microscopic Approach, Parameterized proxy principle, Souslin Tree
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