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