Archives
Keywords
Forcing Axioms Microscopic Approach Cohen real stick HOD coloring number polarized partition relation positive partition relation Slim tree Successor of Singular Cardinal weak diamond Respecting tree Analytic sets Large Cardinals approachability ideal weak Kurepa tree Erdos Cardinal Luzin set L-space Dushnik-Miller Poset Partition Relations Singular Density Chang's conjecture 54G20 transformations SNR Hindman's Theorem Jonsson cardinal xbox Sakurai's Bell inequality Ostaszewski square Knaster stationary hitting Rado's conjecture Dowker space Kurepa Hypothesis Prevalent singular cardinals square principles Selective Ultrafilter Absoluteness Foundations Was Ulam right? Nonspecial tree Fodor-type reflection club_AD indecomposable filter Uniformly homogeneous super-Souslin tree Local Club Condensation. P-Ideal Dichotomy Minimal Walks higher Baire space Singular cardinals combinatorics Distributive tree Ineffable cardinal PFA(S)[S] free Souslin tree Reflecting stationary set Strongly compact cardinal Cardinal function Subadditive Hedetniemi's conjecture Generalized Clubs Commutative projection system Rock n' Roll Universal Sequences Filter reflection stationary reflection Rainbow sets Chromatic number Hereditarily Lindelöf space projective Boolean algebra Sierpinski's onto mapping principle Shelah's Strong Hypothesis unbounded function square countably metacompact regressive Souslin tree Souslin Tree sap Square-Brackets Partition Relations specializable Souslin tree Diamond-sharp tensor product graph Diamond Subnormal ideal Amenable C-sequence incompactness Almost Souslin Strong coloring reflection principles nonmeager set Mandelbrot set Precaliber middle diamond Knaster and friends ZFC construction Subtle tree property full tree Coherent tree Non-saturation Aronszajn tree free Boolean algebra Sigma-Prikry Diamond for trees Small forcing Uniformization Generalized descriptive set theory Singular cofinality diamond star b-scale Countryman line OCA Almost countably chromatic Well-behaved magma strongly bounded groups Successor of Regular Cardinal Vanishing levels Martin's Axiom Axiom R Weakly compact cardinal Parameterized proxy principle Commutative cancellative semigroups Fast club Open Access Ascent Path S-Space ccc Cardinal Invariants Constructible Universe Closed coloring GMA Whitehead Problem Subtle cardinal weak square Club Guessing Postprocessing function Ulam matrix Almost-disjoint family very good scale AIM forcing Forcing Intersection model Fat stationary set C-sequence O-space Reduced Power Uniformly coherent Lipschitz reduction Erdos-Hajnal graphs Antichain Strongly Luzin set Ramsey theory over partitions Prikry-type forcing Greatly Mahlo Iterated forcing PFA
Tag Archives: 03E35
A forcing axiom deciding the generalized Souslin Hypothesis
Joint work with Chris Lambie-Hanson. Abstract. We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, Souslin Tree, square, super-Souslin tree
1 Comment
Reflection on the coloring and chromatic numbers
Joint work with Chris Lambie-Hanson. Abstract. We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) … Continue reading
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Chang's conjecture, Chromatic number, coloring number, Fodor-type reflection, incompactness, Iterated forcing, Parameterized proxy principle, Postprocessing function, Rado's conjecture, square, stationary reflection
2 Comments
Strong failures of higher analogs of Hindman’s Theorem
Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
1 Comment
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
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
Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a
Same Graph, Different Universe
Abstract. May the same graph admit two different chromatic numbers in two different universes? how about infinitely many different values? and can this be achieved without changing the cardinals structure? In this paper, it is proved that in Godel’s constructible … Continue reading
Posted in Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, approachability ideal, Chromatic number, Constructible Universe, Forcing, Ostaszewski square
10 Comments
Chromatic numbers of graphs – large gaps
Abstract. We say that a graph
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Almost countably chromatic, Chromatic number, incompactness, Ostaszewski square
6 Comments
Jensen’s diamond principle and its relatives
This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading
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
