### 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
- Genearlizations 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

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

# 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