### Archives

### Recent blog posts

- Prikry forcing may 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

### Keywords

PFA(S)[S] free Boolean algebra Successor of Regular Cardinal Ascent Path Selective Ultrafilter Diamond stationary hitting Aronszajn tree Dushnik-Miller Slim tree Hereditarily Lindelöf space Martin's Axiom Club Guessing Rainbow sets Successor of Singular Cardinal Whitehead Problem Reduced Power Jonsson cardinal Singular Density ccc Singular cardinals combinatorics Rock n' Roll approachability ideal diamond star Square-Brackets Partition Relations Chang's conjecture Poset Erdos-Hajnal graphs S-Space Prevalent singular cardinals reflection principles Small forcing Chromatic number weak square Weakly compact cardinal Shelah's Strong Hypothesis square Kurepa Hypothesis Ostaszewski square incompactness Prikry-type forcing Uniformization 05D10 Rado's conjecture Microscopic Approach Constructible Universe projective Boolean algebra 20M14 Cardinal function PFA polarized partition relation Mandelbrot set very good scale Souslin Tree coloring number Almost Souslin Knaster weak diamond Large Cardinals Almost-disjoint famiy Generalized Clubs 05A17 Universal Sequences Singular Cofinality b-scale Singular coﬁnality Fat stationary set Fast club Foundations Axiom R Partition Relations Erdos Cardinal 11P99 stationary reflection Antichain HOD tensor product graph Cardinal Invariants middle diamond Coherent tree Cohen real Forcing Axioms Fodor-type reflection L-space Almost countably chromatic OCA xbox Absoluteness P-Ideal Dichotomy Non-saturation Stevo Todorcevic Forcing Sakurai's Bell inequality Hedetniemi's conjecture Hindman's Theorem Minimal Walks Parameterized proxy principle Commutative cancellative semigroups sap

# Tag Archives: Prikry-type forcing

## More notions of forcing add a Souslin tree

Joint work with Ari Meir Brodsky. Abstract. An $\aleph_1$-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But 15 years after Tennenbaum and independently Jech devised notions of forcing for introducing … Continue reading

## Prikry forcing may add a Souslin tree

A celebrated theorem of Shelah states that adding a Cohen real introduces a Souslin tree. Are there any other examples of notions of forcing that add a $\kappa$-Souslin tree? and why is this of interest? My motivation comes from a … Continue reading

## Prikry Forcing

Recall that the chromatic number of a (symmetric) graph $(G,E)$, denoted $\text{Chr}(G,E)$, is the least (possible finite) cardinal $\kappa$, for which there exists a coloring $c:G\rightarrow\kappa$ such that $gEh$ entails $c(g)\neq c(h)$. Given a forcing notion $\mathbb P$, it is … Continue reading