### 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

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

# 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