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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

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

# 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