### 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

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

# 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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