### 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

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

# 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 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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