### 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

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

# Category Archives: Preprints

## The eightfold way

Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. Three central combinatorial properties in set theory are the tree property, the approachability property and stationary reflection. We prove the mutual independence of these properties by showing … 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

## Ordinal definable subsets of singular cardinals

Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. A remarkable result by Shelah states that if $\kappa$ is a singular strong limit cardinal of uncountable cofinality then there is a subset $x$ of $\kappa$ such … Continue reading

Posted in Preprints, Singular Cardinals Combinatorics
Tagged HOD, Singular cardinals combinatorics
1 Comment

## 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
3 Comments