### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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