### 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
- 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
- Partitioning the club guessing January 22, 2014

### Keywords

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

# 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