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