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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

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

# Tag Archives: Parameterized proxy principle

## A remark on Schimmerling’s question

Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading

## 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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