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- 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

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

# Tag Archives: Ostaszewski square

## Same Graph, Different Universe

Abstract. May the same graph admit two different chromatic numbers in two different universes? how about infinitely many different values? and can this be achieved without changing the cardinals structure? In this paper, it is proved that in Godel’s constructible … Continue reading

Posted in Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, approachability ideal, Chromatic number, Constructible Universe, Forcing, Ostaszewski square
10 Comments

## Hedetniemi’s conjecture for uncountable graphs

Abstract. It is proved that in Godel’s constructible universe, for every successor cardinal $\kappa$, there exist graphs $\mathcal G$ and $\mathcal H$ of size and chromatic number $\kappa$, for which the tensor product graph $\mathcal G\times\mathcal H$ is countably chromatic. … Continue reading

## Chromatic numbers of graphs – large gaps

Abstract. We say that a graph $G$ is $(\aleph_0,\kappa)$-chromatic if $\text{Chr}(G)=\kappa$, while $\text{Chr}(G’)\le\aleph_0$ for any subgraph $G’$ of $G$ of size $<|G|$. The main result of this paper reads as follows. If $\square_\lambda+\text{CH}_\lambda$ holds for a given uncountable cardinal $\lambda$, … Continue reading

Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Almost countably chromatic, Chromatic number, incompactness, Ostaszewski square
6 Comments

## The Ostaszewski square, and homogeneous Souslin trees

Abstract: Assume GCH and let $\lambda$ denote an uncountable cardinal. We prove that if $\square_\lambda$ holds, then this may be witnessed by a coherent sequence $\left\langle C_\alpha \mid \alpha<\lambda^+\right\rangle$ with the following remarkable guessing property: For every sequence $\langle A_i\mid i<\lambda\rangle$ … Continue reading

Posted in Publications, Souslin Hypothesis, Squares and Diamonds
Tagged 03E05, 03E35, Club Guessing, Fat stationary set, Ostaszewski square, Souslin Tree
5 Comments