### Archives

### 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

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

# Tag Archives: Parameterized proxy principle

## A remark on Schimmerling’s question

Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading

## 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