Archives
Keywords
Diamond for trees Singular Density Diamond 54G20 Ineffable cardinal diamond star Commutative projection system Was Ulam right? Rainbow sets Generalized Clubs P-Ideal Dichotomy Analytic sets Respecting tree Rock n' Roll PFA(S)[S] higher Baire space free Souslin tree Uniformization nonmeager set Small forcing Local Club Condensation. Erdos-Hajnal graphs Universal Sequences very good scale Cardinal function Fast club Lipschitz reduction polarized partition relation Reflecting stationary set Strongly Luzin set Non-saturation unbounded function Coherent tree square principles HOD Knaster Subnormal ideal Ramsey theory over partitions Successor of Regular Cardinal indecomposable filter Parameterized proxy principle ccc sap Luzin set middle diamond Subtle tree property Axiom R Foundations incompactness regressive Souslin tree Postprocessing function Mandelbrot set Greatly Mahlo Open Access Distributive tree Hereditarily Lindelöf space xbox full tree Commutative cancellative semigroups Iterated forcing Subtle cardinal Countryman line Square-Brackets Partition Relations Dushnik-Miller Well-behaved magma Dowker space Nonspecial tree stationary reflection Poset reflection principles Sakurai's Bell inequality Constructible Universe Chromatic number Almost countably chromatic Strong coloring Amenable C-sequence C-sequence Reduced Power Aronszajn tree GMA transformations strongly bounded groups Erdos Cardinal positive partition relation Partition Relations Weakly compact cardinal Martin's Axiom SNR Intersection model Absoluteness Cardinal Invariants Uniformly homogeneous square projective Boolean algebra S-Space Ostaszewski square weak Kurepa tree Subadditive Large Cardinals PFA weak square Club Guessing club_AD Closed coloring Vanishing levels Sigma-Prikry stick Successor of Singular Cardinal tensor product graph Forcing Axioms Strongly compact cardinal Singular cofinality Ulam matrix Ascent Path Kurepa Hypothesis Knaster and friends Prikry-type forcing Precaliber Forcing Almost Souslin Singular cardinals combinatorics Slim tree b-scale Diamond-sharp Sierpinski's onto mapping principle weak diamond Microscopic Approach OCA L-space AIM forcing Chang's conjecture Hedetniemi's conjecture Rado's conjecture Fat stationary set Selective Ultrafilter Shelah's Strong Hypothesis Souslin Tree Antichain Almost-disjoint family O-space free Boolean algebra Whitehead Problem Filter reflection countably metacompact Minimal Walks Fodor-type reflection Prevalent singular cardinals specializable Souslin tree Generalized descriptive set theory Hindman's Theorem Jonsson cardinal coloring number super-Souslin tree stationary hitting Uniformly coherent approachability ideal ZFC construction Cohen real
Tag Archives: Souslin Tree
Prikry forcing may add a Souslin tree
A celebrated theorem of Shelah states that adding a Cohen real introduces a Souslin tree. Are there any other examples of notions of forcing that add a
Higher Souslin trees and the GCH, revisited
Abstract. It is proved that for every uncountable cardinal
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, Open Access, regressive Souslin tree, Souslin Tree, square, Weakly compact cardinal, xbox
16 Comments
Prolific Souslin trees
In a paper from 1971, Erdos and Hajnal asked whether (assuming CH) every coloring witnessing
Posted in Blog, Expository
Tagged Rainbow sets, Souslin Tree, Square-Brackets Partition Relations
Leave a comment
A microscopic approach to Souslin-tree constructions. Part I
Joint work with Ari Meir Brodsky. Abstract. We propose a parameterized proxy principle from which
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E65, 05C05, Coherent tree, Diamond, Microscopic Approach, Parameterized proxy principle, Slim tree, Souslin Tree, square, xbox
5 Comments
P.O.I. Workshop in pure and descriptive set theory, September 2015
I gave an invited talk at the P.O.I Workshop in pure and descriptive set theory, Torino, September 26, 2015. Title:
Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a
Forcing and its Applications Retrospective Workshop, April 2015
I gave an invited talk at Forcing and its Applications Retrospective Workshop, Toronto, April 1st, 2015. Title: A microscopic approach to Souslin trees constructions Abstract: We present an approach to construct
Posted in Invited Talks
Tagged Microscopic Approach, Parameterized proxy principle, Souslin Tree
Leave a comment
Forcing with a Souslin tree makes
I was meaning to include a proof of Farah’s lemma in my previous post, but then I realized that the slick proof assumes some background which may worth spelling out, first. Therefore, I am dedicating a short post for a … Continue reading
Forcing with a Souslin tree makes
I was meaning to include a proof of Farah’s lemma in my previous post, but then I realized that the slick proof assumes some background which may worth spelling out, first. Therefore, I am dedicating a short post for a … Continue reading
The P-Ideal Dichotomy and the Souslin Hypothesis
John Krueger is visiting Toronto these days, and in a conversation today, we asked ourselves how do one prove the Abraham-Todorcevic theorem that PID implies SH. Namely, that the next statement implies that there are no Souslin trees: Definition. The … Continue reading