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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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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