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

# 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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