Archives
Keywords
Mandelbrot set Luzin set Antichain Closed coloring Cardinal Invariants Analytic sets regressive Souslin tree Small forcing Ulam matrix Rock n' Roll transformations Uniformly coherent Foundations Sakurai's Bell inequality 54G20 approachability ideal Generalized descriptive set theory xbox square tensor product graph Chromatic number Microscopic Approach reflection principles Partition Relations Kurepa Hypothesis PFA Coherent tree Postprocessing function club_AD unbounded function Erdos Cardinal Prevalent singular cardinals countably metacompact Fast club Rainbow sets specializable Souslin tree Prikry-type forcing Generalized Clubs Intersection model Universal Sequences Chang's conjecture SNR Fodor-type reflection Strongly Luzin set polarized partition relation middle diamond P-Ideal Dichotomy Ascent Path Dushnik-Miller Poset incompactness ccc positive partition relation L-space Almost-disjoint family Ineffable cardinal indecomposable ultrafilter Forcing coloring number Hedetniemi's conjecture Axiom R Well-behaved magma GMA Reflecting stationary set Cardinal function Commutative cancellative semigroups full tree Successor of Singular Cardinal Diamond Knaster and friends Minimal Walks square principles weak Kurepa tree weak square Greatly Mahlo Non-saturation Selective Ultrafilter Lipschitz reduction projective Boolean algebra Parameterized proxy principle Sierpinski's onto mapping principle super-Souslin tree Aronszajn tree higher Baire space b-scale Weakly compact cardinal Singular cardinals combinatorics Subadditive Successor of Regular Cardinal stationary reflection O-space Almost Souslin Shelah's Strong Hypothesis Open Access Forcing Axioms free Boolean algebra Local Club Condensation. Respecting tree Reduced Power Amenable C-sequence Diamond for trees Almost countably chromatic Constructible Universe Subtle tree property Ramsey theory over partitions Absoluteness Commutative projection system Strong coloring S-Space Slim tree Nonspecial tree Diamond-sharp Rado's conjecture stationary hitting Cohen real OCA very good scale Countryman line PFA(S)[S] Souslin Tree Singular Density Singular cofinality Whitehead Problem Subnormal ideal Hereditarily Lindelöf space Large Cardinals Jonsson cardinal Subtle cardinal Sigma-Prikry ZFC construction free Souslin tree Iterated forcing sap Precaliber Uniformization C-sequence Was Ulam right Erdos-Hajnal graphs strongly bounded groups HOD diamond star Square-Brackets Partition Relations AIM forcing Dowker space Knaster Hindman's Theorem nonmeager set Uniformly homogeneous Filter reflection Strongly compact cardinal Vanishing levels weak diamond Martin's Axiom Fat stationary set stick Ostaszewski square Distributive tree Club Guessing
Tag Archives: Minimal Walks
MFO workshop in Set Theory, January 2014
I gave an invited talk at the Set Theory workshop in Obwerwolfach, January 2014. Talk Title: Complicated Colorings. Abstract: If $\lambda,\kappa$ are regular cardinals, $\lambda>\kappa^+$, and $E^{\lambda}_{\ge\kappa}$ admits a nonreflecting stationary set, then $\text{Pr}_1(\lambda,\lambda,\lambda,\kappa)$ holds. Downloads:
Walk on countable ordinals: the characteristics
In this post, we shall present a few aspects of the method of walk on ordinals (focusing on countable ordinals), record its characteristics, and verify some of their properties. All definitions and results in this post are due to Todorcevic. … Continue reading
Rectangular square-bracket operation for successor of regular cardinals
Joint work with Stevo Todorcevic. Extended Abstract: Consider the coloring statement $\lambda^+\nrightarrow[\lambda^+;\lambda^+]^2_{\lambda^+}$ for a given regular cardinal $\lambda$: In 1990, Shelah proved the above for $\lambda>2^{\aleph_0}$; In 1991, Shelah proved the above for $\lambda>\aleph_1$; In 1997, Shelah proved the above … 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 $\lambda$ asserts the existence of a particular ladder … Continue reading
Transforming rectangles into squares, with applications to strong colorings
Abstract: It is proved that every singular cardinal $\lambda$ admits a function $\textbf{rts}:[\lambda^+]^2\rightarrow[\lambda^+]^2$ that transforms rectangles into squares. That is, whenever $A,B$ are cofinal subsets of $\lambda^+$, we have $\textbf{rts}[A\circledast B]\supseteq C\circledast C$, for some cofinal subset $C\subseteq\lambda^+$. As a … Continue reading
