### 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

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

# 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