### Archives

### 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

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

# Tag Archives: 03E57

## 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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## A forcing axiom deciding the generalized Souslin Hypothesis

Joint work with Chris Lambie-Hanson. Abstract. We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal $\lambda$, … Continue reading

Posted in Preprints, Souslin Hypothesis
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, Souslin Tree, square, super-Souslin tree
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