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