### 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

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

# 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