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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations 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

### Keywords

Prikry-type forcing Microscopic Approach Fat stationary set OCA Non-saturation 11P99 sap Club Guessing Aronszajn tree Dushnik-Miller Hereditarily Lindelöf space Successor of Regular Cardinal Axiom R Shelah's Strong Hypothesis Rock n' Roll free Boolean algebra weak square Absoluteness Large Cardinals Weakly compact cardinal Antichain Fodor-type reflection Cardinal Invariants stationary hitting xbox Chromatic number square principles approachability ideal very good scale Postprocessing function 05A17 Constructible Universe weak diamond Whitehead Problem Luzin set Forcing Distributive tree HOD Jonsson cardinal Chang's conjecture Generalized Clubs Hindman's Theorem PFA stationary reflection Reduced Power free Souslin tree Cardinal function Ostaszewski square Coherent tree Poset Uniformly coherent Ascent Path ccc diamond star Parameterized proxy principle Rainbow sets Forcing Axioms Small forcing coloring number tensor product graph PFA(S)[S] specializable Souslin tree Souslin Tree Erdos Cardinal S-Space Rado's conjecture Selective Ultrafilter Almost-disjoint famiy Square-Brackets Partition Relations L-space Singular Density Cohen real Hedetniemi's conjecture Partition Relations Slim tree middle diamond projective Boolean algebra P-Ideal Dichotomy Singular cardinals combinatorics super-Souslin tree Mandelbrot set Knaster Almost countably chromatic Stevo Todorcevic Foundations Uniformization Singular coﬁnality Minimal Walks Successor of Singular Cardinal Commutative cancellative semigroups Erdos-Hajnal graphs Universal Sequences Almost Souslin Diamond b-scale Kurepa Hypothesis Prevalent singular cardinals reflection principles Martin's Axiom Nonspecial tree Fast club incompactness Sakurai's Bell inequality square polarized partition relation

# Tag Archives: weak square

## A remark on Schimmerling’s question

## Weak square and stationary reflection

Joint work with Gunter Fuchs. Abstract. It is well-known that the square principle $\square_\lambda$ entails the existence of a non-reflecting stationary subset of $\lambda^+$, whereas the weak square principle $\square^*_\lambda$ does not. Here we show that if $\mu^{cf(\lambda)}<\lambda$ for all $\mu<\lambda$, … Continue reading

Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, stationary reflection, weak square
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## The search for diamonds

Abstract: This is a review I wrote for the Bulletin of Symbolic Logic on the following papers: Saharon Shelah, Middle Diamond, Archive for Mathematical Logic, vol. 44 (2005), pp. 527–560. Saharon Shelah, Diamonds, Proceedings of the American Mathematical Society, vol. … Continue reading

Posted in Publications, Reviews, Squares and Diamonds
Tagged Diamond, middle diamond, weak diamond, weak square
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## A cofinality-preserving small forcing may introduce a special Aronszajn tree

Extended Abstract: Shelah proved that Cohen forcing introduces a Souslin tree; Jensen proved that a c.c.c. forcing may consistently add a Kurepa tree; Todorcevic proved that a Knaster poset may already force the Kurepa hypothesis; Irrgang introduced a c.c.c. notion … Continue reading

Posted in Publications, Squares and Diamonds
Tagged 03E04, 03E05, 03E35, Aronszajn tree, Small forcing, Successor of Singular Cardinal, weak square
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## Young Researchers in Set Theory, March 2011

These are the slides of a talk I gave at the Young Researchers in Set Theory 2011 meeting (Königswinter, 21–25 March 2011). Talk Title: Around Jensen’s square principle Abstract: Jensen‘s square principle for a cardinal $\lambda$ asserts the existence of a particular ladder … Continue reading