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- Prolific Souslin trees March 17, 2016
- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
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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

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

# 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