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