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

# 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