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

# 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