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