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