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### 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

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

# 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