### 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

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