### 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

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

# Tag Archives: Forcing Axioms

## 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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## Bell’s theorem on the cardinal invariant $\mathfrak p$

In this post, we shall provide a proof to a famous theorem of Murray Bell stating that $MA_\kappa(\text{the class of }\sigma\text{-centered posets})$ holds iff $\kappa<\mathfrak p$. We commence with defining the cardinal invariant $\mathfrak p$. For sets $A$ and $B$, … Continue reading