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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

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

# 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