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- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- 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
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

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

# 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