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