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Minimal Walks Parameterized proxy principle Fat stationary set PFA(S)[S] Small forcing Amenable C-sequence Rainbow sets GMA Almost countably chromatic Ascent Path square Intersection model Uniformization Erdos Cardinal Singular cardinals combinatorics Local Club Condensation. Large Cardinals super-Souslin tree Closed coloring club_AD Singular Density AIM forcing Diamond-sharp ZFC construction Selective Ultrafilter Poset incompactness Absoluteness Filter reflection very good scale Ostaszewski square xbox free Boolean algebra Sigma-Prikry weak square Fodor-type reflection OCA Subtle tree property Reduced Power indecomposable ultrafilter Diamond for trees Martin's Axiom middle diamond Respecting tree SNR Antichain specializable Souslin tree nonmeager set Reflecting stationary set Sakurai's Bell inequality Ineffable cardinal Uniformly coherent Postprocessing function Whitehead Problem Erdos-Hajnal graphs ccc projective Boolean algebra Fast club Constructible Universe Axiom R Hereditarily Lindelöf space reflection principles Almost Souslin Cohen real coloring number Club Guessing polarized partition relation Sierpinski's onto mapping principle Successor of Regular Cardinal Shelah's Strong Hypothesis Coherent tree Forcing Axioms Uniformly homogeneous Greatly Mahlo Foundations L-space Non-saturation Souslin Tree Countryman line Subtle cardinal Commutative cancellative semigroups Was Ulam right Dowker space C-sequence Forcing Aronszajn tree Lipschitz reduction Slim tree regressive Souslin tree Jonsson cardinal Successor of Singular Cardinal Strongly compact cardinal PFA Mandelbrot set HOD Nonspecial tree Chang's conjecture Distributive tree Microscopic Approach Precaliber Subadditive stationary hitting Kurepa Hypothesis Prikry-type forcing Strong coloring Vanishing levels transformations Strongly Luzin set Dushnik-Miller Luzin set S-Space Almost-disjoint family O-space higher Baire space Knaster approachability ideal positive partition relation Weakly compact cardinal stick Generalized Clubs Rock n' Roll Subnormal ideal stationary reflection weak Kurepa tree diamond star strongly bounded groups Open Access Iterated forcing Knaster and friends Generalized descriptive set theory weak diamond Ramsey theory over partitions unbounded function Rado's conjecture Analytic sets Well-behaved magma Commutative projection system Partition Relations Diamond Prevalent singular cardinals Square-Brackets Partition Relations Cardinal function 54G20 tensor product graph Singular cofinality Ulam matrix full tree Hindman's Theorem square principles Universal Sequences sap free Souslin tree Cardinal Invariants P-Ideal Dichotomy b-scale Chromatic number countably metacompact Hedetniemi's conjecture
Blog Archives
Proxy principles in combinatorial set theory
Joint work with Ari Meir Brodsky and Shira Yadai. Abstract. The parameterized proxy principles were introduced by Brodsky and Rinot in a 2017 paper as new foundations for the construction of $\kappa$-Souslin trees in a uniform way that does not … 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
Distributive Aronszajn trees
Joint work with Ari Meir Brodsky. Abstract. Ben-David and Shelah proved that if $\lambda$ is a singular strong-limit cardinal and $2^\lambda=\lambda^+$, then $\square^*_\lambda$ entails the existence of a $\lambda$-distributive $\lambda^+$-Aronszajn tree. Here, it is proved that the same conclusion remains … Continue reading
More notions of forcing add a Souslin tree
Joint work with Ari Meir Brodsky. Abstract. An $\aleph_1$-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But 15 years after Tennenbaum and independently Jech devised notions of forcing for introducing … 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
