### 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

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

# 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
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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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