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