### 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

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

# 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