### 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

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

# 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