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### 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

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

# 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