Archives
Keywords
Ascending path coloring number polarized partition relation Hereditarily Lindelöf space O-space Hindman's Theorem Uniformly homogeneous Subtle tree property Ineffable cardinal Strongly Luzin set perfectly normal Whitehead Problem Chromatic number Selective Ultrafilter Antichain Cardinal Invariants Shelah's Strong Hypothesis stationary hitting S-Space b-scale Respecting tree Forcing with side conditions Postprocessing function weak diamond Fast club Strong coloring Almost countably chromatic diamond star Successor of Regular Cardinal Lipschitz reduction Weakly compact cardinal middle diamond Nonspecial tree countably metacompact Knaster and friends Well-behaved magma Was Ulam right? Erdos-Hajnal graphs tensor product graph reflection principles Souslin Tree regressive Souslin tree Mandelbrot set positive partition relation Chang's conjecture Singular Density Kurepa Hypothesis Distributive tree Countryman line SNR Luzin set Precaliber Cardinal function Club Guessing Dushnik-Miller specializable Souslin tree projective Boolean algebra Diamond Forcing Commutative projection system Fat stationary set square principles Prevalent singular cardinals Foundations Subnormal ideal GMA nonmeager set Dowker space Aronszajn tree Universal Sequences Forcing Axioms club_AD Non-saturation indecomposable filter Singular cofinality Diamond-sharp Knaster Almost-disjoint family very good scale Jonsson cardinal Absoluteness Almost Souslin Slim tree Monotonically far Iterated forcing Entangled linear order Partition relations for trees Microscopic Approach Prikry-type forcing free Boolean algebra Uniformization HOD weak square free Souslin tree full tree Sigma-Prikry Parameterized proxy principle P-Ideal Dichotomy higher Baire space Generalized Clubs square sap strongly bounded groups C-sequence Fodor-type reflection Greatly Mahlo Small forcing Rock n' Roll PFA Square-Brackets Partition Relations Successor of Singular Cardinal Erdos Cardinal Interval topology on trees incompactness Subtle cardinal Ascent Path Generalized descriptive set theory Analytic sets unbounded function ccc Partition Relations Filter reflection transformations approachability ideal stick Amenable C-sequence Coherent tree Cohen real Reduced Power Sierpinski's onto mapping principle Uniformly coherent AIM forcing xbox Subadditive ZFC construction Sakurai's Bell inequality Large Cardinals Hedetniemi's conjecture Strongly compact cardinal Martin's Axiom Closed coloring Diamond for trees 54G20 Ramsey theory over partitions Ostaszewski square L-space Ulam matrix Minimal Walks Singular cardinals combinatorics Open Access super-Souslin tree Local Club Condensation. Commutative cancellative semigroups Rainbow sets Poset stationary reflection Rado's conjecture OCA Vanishing levels weak Kurepa tree PFA(S)[S] Constructible Universe Reflecting stationary set Axiom R Intersection model
Tag Archives: square principles
More notions of forcing add a square
Joint work with Yair Hayut and Zhixing You. Abstract. Foreman and Magidor showed that the continuum hypothesis implies the existence of a countably-closed $\aleph_2$-cc forcing notion $\mathbb P$ for adding $\square_{\omega_1}$. Here, we show that $\mathbb P$ may consistently be … Continue reading
Posted in Squares and Diamonds
Tagged full tree, Souslin Tree, square principles, super-Souslin tree
Comments Off on More notions of forcing add a square
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
