### 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

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

# 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