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- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- 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

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

# 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