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weak Kurepa tree square principles approachability ideal stationary hitting S-Space Countryman line full tree Chang's conjecture indecomposable ultrafilter Ramsey theory over partitions Commutative projection system Knaster Amenable C-sequence Luzin set reflection principles Diamond-sharp coloring number Selective Ultrafilter weak square Erdos Cardinal Commutative cancellative semigroups polarized partition relation Universal Sequences unbounded function diamond star Microscopic Approach O-space middle diamond Generalized Clubs Square-Brackets Partition Relations Minimal Walks Rainbow sets positive partition relation Almost Souslin Sakurai's Bell inequality Nonspecial tree Shelah's Strong Hypothesis Uniformly coherent Small forcing Erdos-Hajnal graphs Constructible Universe Intersection model stick Rado's conjecture Subadditive Prevalent singular cardinals Cardinal function Dowker space Jonsson cardinal specializable Souslin tree Lipschitz reduction free Boolean algebra HOD free Souslin tree Chromatic number Subnormal ideal Singular cofinality Martin's Axiom Successor of Regular Cardinal Coherent tree Poset Diamond for trees Large Cardinals Fodor-type reflection Local Club Condensation. Subtle tree property Ascent Path Ineffable cardinal Souslin Tree Non-saturation xbox Knaster and friends Vanishing levels Iterated forcing Sigma-Prikry square Uniformization Hedetniemi's conjecture Forcing higher Baire space Analytic sets Antichain Sierpinski's onto mapping principle SNR Uniformly homogeneous Distributive tree countably metacompact regressive Souslin tree weak diamond Successor of Singular Cardinal strongly bounded groups projective Boolean algebra Well-behaved magma Diamond PFA(S)[S] Cardinal Invariants Whitehead Problem Reflecting stationary set Cohen real Forcing Axioms nonmeager set Filter reflection Parameterized proxy principle ZFC construction Hindman's Theorem P-Ideal Dichotomy Absoluteness Ulam matrix Ostaszewski square 54G20 Almost countably chromatic GMA Greatly Mahlo Slim tree Rock n' Roll tensor product graph Aronszajn tree club_AD super-Souslin tree Kurepa Hypothesis Subtle cardinal Dushnik-Miller Foundations Weakly compact cardinal Hereditarily Lindelöf space b-scale Strongly Luzin set Almost-disjoint family Singular cardinals combinatorics Singular Density C-sequence Partition Relations sap L-space Was Ulam right Respecting tree Strong coloring Mandelbrot set Club Guessing Precaliber incompactness Generalized descriptive set theory OCA Reduced Power Fast club Strongly compact cardinal Postprocessing function Closed coloring Fat stationary set PFA Prikry-type forcing AIM forcing Axiom R stationary reflection transformations ccc very good scale Open Access
Tag Archives: square principles
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
Winter School in Abstract Analysis, January 2023
I gave a 3-lecture tutorial at the Winter School in Abstract Analysis in Steken, January 2023. Title: Club guessing Abstract. Club guessing principles were introduced by Shelah as a weakening of Jensen’s diamond. Most spectacularly, they were used to prove … 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
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
ASL North American Meeting, March 2017
I gave a plenary talk at the 2017 ASL North American Meeting in Boise, March 2017. Talk Title: The current state of the Souslin problem. Abstract: Recall that the real line is that unique separable, dense linear ordering with no endpoints in … Continue reading
