### 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

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

# 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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