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