### 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
- Genearlizations 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

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

# 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 a graph is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large … 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 Preprints, Souslin Hypothesis
Tagged 03E05, 03E35, 03E65, 05C05, Coherent tree, Diamond, Microscopic Approach, Parameterized proxy principle, Slim tree, Souslin Tree, square, xbox
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## 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
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