### 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

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

# Tag Archives: Kurepa Hypothesis

## Strong failures of higher analogs of Hindman’s Theorem

Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … Continue reading

## Square with built-in diamond-plus

Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in $L$ for every infinite cardinal. As an application, we prove that … Continue reading

Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, square, xbox
1 Comment

## Reduced powers of Souslin trees

Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading

## A Kurepa tree from diamond-plus

Recall that $T$ is said to be a $\kappa$-Kurepa tree if $T$ is a tree of height $\kappa$, whose levels $T_\alpha$ has size $\le|\alpha|$ for co-boundedly many $\alpha<\kappa$, and such that the set of branches of $T$ has size $>\kappa$. … Continue reading

## Kurepa trees and ineffable cardinals

## On guessing generalized clubs at the successors of regulars

Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading