### 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

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

# 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