### 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

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