### 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

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

# Category Archives: Preprints

## Distributive Aronszajn trees

Joint work with Ari Meir Brodsky. Abstract. Ben-David and Shelah proved that if $\lambda$ is a singular strong-limit cardinal and $2^\lambda=\lambda^+$, then $\square^*_\lambda$ entails the existence of a $\lambda$-distributive $\lambda^+$-Aronszajn tree. Here, it is proved that the same conclusion remains … Continue reading

## 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
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