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

# 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