### 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

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

# 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