### 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

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

# Tag Archives: Small forcing

## A cofinality-preserving small forcing may introduce a special Aronszajn tree

Extended Abstract: Shelah proved that Cohen forcing introduces a Souslin tree; Jensen proved that a c.c.c. forcing may consistently add a Kurepa tree; Todorcevic proved that a Knaster poset may already force the Kurepa hypothesis; Irrgang introduced a c.c.c. notion … Continue reading

Posted in Publications, Squares and Diamonds
Tagged 03E04, 03E05, 03E35, Aronszajn tree, Small forcing, Successor of Singular Cardinal, weak square
Leave a comment