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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

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

# 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