Archives
Keywords
54G20 Dowker space ccc Knaster Almost-disjoint family Generalized Clubs Prevalent singular cardinals stick Uniformly coherent Successor of Regular Cardinal nonmeager set higher Baire space free Souslin tree Erdos Cardinal Ineffable cardinal Ascent Path Rock n' Roll Forcing Distributive tree stationary reflection Commutative cancellative semigroups Universal Sequences Kurepa Hypothesis Club Guessing Chang's conjecture very good scale Iterated forcing square principles Sigma-Prikry Whitehead Problem Aronszajn tree Strong coloring Was Ulam right? Precaliber Square-Brackets Partition Relations Fat stationary set PFA Commutative projection system L-space Nonspecial tree Slim tree Prikry-type forcing Local Club Condensation. GMA Diamond-sharp Fast club Non-saturation Hindman's Theorem approachability ideal coloring number polarized partition relation AIM forcing incompactness Poset square Hedetniemi's conjecture Respecting tree Diamond Uniformly homogeneous Jonsson cardinal Amenable C-sequence Large Cardinals Souslin Tree Reduced Power Subnormal ideal transformations Ostaszewski square Closed coloring SNR S-Space Luzin set xbox strongly bounded groups indecomposable ultrafilter Rainbow sets Dushnik-Miller Ramsey theory over partitions Almost countably chromatic weak Kurepa tree Small forcing Chromatic number Subadditive Singular cofinality ZFC construction Weakly compact cardinal regressive Souslin tree Strongly Luzin set middle diamond positive partition relation Well-behaved magma club_AD Reflecting stationary set Microscopic Approach Intersection model Subtle cardinal Analytic sets reflection principles Fodor-type reflection Parameterized proxy principle Forcing Axioms OCA b-scale projective Boolean algebra Diamond for trees diamond star Antichain PFA(S)[S] Uniformization O-space super-Souslin tree Open Access Knaster and friends weak diamond countably metacompact P-Ideal Dichotomy Martin's Axiom Generalized descriptive set theory Singular cardinals combinatorics Sierpinski's onto mapping principle Subtle tree property Coherent tree unbounded function Partition Relations Cardinal Invariants Sakurai's Bell inequality Postprocessing function sap Rado's conjecture Vanishing levels Singular Density Greatly Mahlo stationary hitting Successor of Singular Cardinal tensor product graph HOD specializable Souslin tree Mandelbrot set Absoluteness Minimal Walks Lipschitz reduction Axiom R Selective Ultrafilter Countryman line Almost Souslin Ulam matrix Strongly compact cardinal Shelah's Strong Hypothesis Cardinal function free Boolean algebra Erdos-Hajnal graphs Hereditarily Lindelöf space Foundations C-sequence full tree Constructible Universe Filter reflection weak square Cohen real
Tag Archives: Aronszajn tree
Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
11th Young Set Theory Workshop, June 2018
I gave a 4-lecture tutorial at the 11th Young Set Theory Workshop, Lausanne, June 2018. Title: In praise of C-sequences. Abstract. Ulam and Solovay showed that any stationary set may be split into two. Is it also the case that … Continue reading
Posted in Invited Talks
Tagged Aronszajn tree, C-sequence, incompactness, Knaster, Minimal Walks, Postprocessing function, square
Leave a comment
The 14th International Workshop on Set Theory in Luminy, October 2017
I gave an invited talk at the 14th International Workshop on Set Theory in Luminy in Marseille, October 2017. Talk Title: Distributive Aronszajn trees Abstract: It is well-known that that the statement “all
Distributive Aronszajn trees
Joint work with Ari Meir Brodsky. Abstract. Ben-David and Shelah proved that if
The eightfold way
Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. Three central combinatorial properties in set theory are the tree property, the approachability property and stationary reflection. We prove the mutual independence of these properties by showing … Continue reading
Chain conditions of products, and weakly compact cardinals
Abstract. The history of productivity of the
Posted in Partition Relations, Publications
Tagged Aronszajn tree, ccc, Fat stationary set, Minimal Walks, square, Weakly compact cardinal
2 Comments
PFA and the tree property at
Recall that a poset
A cofinality-preserving small forcing may introduce a special Aronszajn tree
Extended Abstract: Shelah proved that Cohen forcing introduces a Souslin tree; Jensen proved that a c.c.c. forcing may consistently add a Kurepa tree; Todorcevic proved that a Knaster poset may already force the Kurepa hypothesis; Irrgang introduced a c.c.c. notion … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E04, 03E05, 03E35, Aronszajn tree, Small forcing, Successor of Singular Cardinal, weak square
Leave a comment
