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