Archives
Keywords
Constructible Universe Cardinal Invariants Mandelbrot set middle diamond Club Guessing Selective Ultrafilter higher Baire space Almost-disjoint family PFA(S)[S] Fat stationary set Sierpinski's onto mapping principle weak diamond AIM forcing Analytic sets Sakurai's Bell inequality Luzin set Small forcing Aronszajn tree sap Square-Brackets Partition Relations Uniformly homogeneous Erdos-Hajnal graphs Coherent tree Subadditive Axiom R projective Boolean algebra Knaster Ulam matrix Absoluteness Microscopic Approach Knaster and friends 54G20 Was Ulam right? Chang's conjecture Local Club Condensation. Singular cardinals combinatorics nonmeager set Partition Relations reflection principles polarized partition relation ZFC construction Successor of Singular Cardinal Cardinal function Hindman's Theorem very good scale Martin's Axiom Respecting tree Prikry-type forcing Forcing Axioms indecomposable ultrafilter Amenable C-sequence xbox Cohen real Shelah's Strong Hypothesis Lipschitz reduction Postprocessing function Greatly Mahlo Well-behaved magma SNR Antichain specializable Souslin tree Kurepa Hypothesis P-Ideal Dichotomy Generalized descriptive set theory Rado's conjecture Commutative cancellative semigroups square principles Parameterized proxy principle stationary reflection incompactness stationary hitting L-space Foundations free Boolean algebra Intersection model Reduced Power Diamond O-space Jonsson cardinal Chromatic number full tree Souslin Tree Vanishing levels Commutative projection system Erdos Cardinal Hereditarily Lindelöf space Sigma-Prikry Uniformization Countryman line super-Souslin tree Diamond for trees C-sequence free Souslin tree Almost Souslin Uniformly coherent unbounded function Distributive tree Dushnik-Miller stick Dowker space b-scale strongly bounded groups Filter reflection Non-saturation Hedetniemi's conjecture Strong coloring Ramsey theory over partitions Singular Density tensor product graph Subtle tree property Successor of Regular Cardinal S-Space Subtle cardinal Iterated forcing OCA approachability ideal regressive Souslin tree Nonspecial tree weak square Fodor-type reflection club_AD Generalized Clubs Weakly compact cardinal weak Kurepa tree Ostaszewski square Precaliber Reflecting stationary set Whitehead Problem Subnormal ideal Forcing Ineffable cardinal Strongly Luzin set coloring number Singular cofinality Closed coloring ccc Open Access Rock n' Roll HOD transformations Poset square Fast club Minimal Walks Almost countably chromatic Large Cardinals GMA positive partition relation Rainbow sets countably metacompact diamond star Diamond-sharp Prevalent singular cardinals Strongly compact cardinal Universal Sequences Ascent Path PFA Slim tree
Tag Archives: square
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
Square with built-in diamond-plus
Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, Respecting tree, square, xbox
1 Comment
Putting a diamond inside the square
Abstract. By a 35-year-old theorem of Shelah,
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Diamond, square, Successor of Singular Cardinal
1 Comment
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
Square principles
Since the birth of Jensen’s original Square principle, many variations of the principle were introduced and intensively studied. Asaf Karagila suggested me today to put some order into all of these principles. Here is a trial. Definition. A square principle … Continue reading
The order-type of clubs in a square sequence
Recall Jensen’s notion of square: Definition (Jensen): For an infinite cardinal
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
Young Researchers in Set Theory, March 2011
These are the slides of a talk I gave at the Young Researchers in Set Theory 2011 meeting (Königswinter, 21–25 March 2011). Talk Title: Around Jensen’s square principle Abstract: Jensen‘s square principle for a cardinal
The failure of diamond on a reflecting stationary set
Joint work with Moti Gitik. Abstract: It is shown that the failure of
