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- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013
- Gabriel Belachsan (14/5/1976 – 20/8/2013) August 20, 2013

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Cardinal Invariants Universal Sequences ccc Dushnik-Miller Weakly compact cardinal Constructible Universe Kurepa Hypothesis very good scale Large Cardinals weak square Sakurai's Bell inequality Knaster Antichain Minimal Walks approachability ideal middle diamond Hedetniemi's conjecture polarized partition relation Uniformization Rock n' Roll Cohen real Diamond Erdos Cardinal Poset Small forcing Almost-disjoint famiy S-Space tensor product graph incompactness Foundations Club Guessing Rainbow sets Square-Brackets Partition Relations weak diamond Martin's Axiom free Boolean algebra Successor of Singular Cardinal OCA Aronszajn tree Rado's conjecture reflection principles square Forcing Absoluteness Shelah's Strong Hypothesis b-scale Successor of Regular Cardinal Ostaszewski square Prikry-type forcing stationary reflection Singular Cofinality PFA(S)[S] Erdos-Hajnal graphs Almost countably chromatic projective Boolean algebra Chromatic number Non-saturation sap Mandelbrot set stationary hitting Singular Density Cardinal function Axiom R Forcing Axioms Hereditarily Lindelöf space Souslin Tree PFA Singular cardinals combinatorics Whitehead Problem L-space Generalized Clubs Partition Relations diamond star Prevalent singular cardinals P-Ideal Dichotomy

# Tag Archives: 03E02

## 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

## 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