### 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

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

# Tag Archives: Parameterized proxy principle

## Reflection on the coloring and chromatic numbers

Joint work with Chris Lambie-Hanson. Abstract. We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) … Continue reading

## 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

## A Microscopic approach to Souslin-tree constructions. Part I

Joint work with Ari Meir Brodsky. Abstract. We propose a parameterized proxy principle from which $\kappa$-Souslin trees with various additional features can be constructed, regardless of the identity of $\kappa$. We then introduce the microscopic approach, which is a simple … Continue reading

Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E65, 05C05, Coherent tree, Diamond, Microscopic Approach, Parameterized proxy principle, Slim tree, Souslin Tree, square, xbox
4 Comments

## Forcing and its Applications Retrospective Workshop, April 2015

I gave an invited talk at Forcing and its Applications Retrospective Workshop, Toronto, April 1st, 2015. Title: A microscopic approach to Souslin trees constructions Abstract: We present an approach to construct $\kappa$-Souslin trees that is insensitive to the identity of … Continue reading

Posted in Invited Talks
Tagged Microscopic Approach, Parameterized proxy principle, Souslin Tree
Leave a comment