### 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

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

# 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