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