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