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