Wyniki wyszukiwania - BazTech

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 2023

Powiadomienia systemowe

Sesja wygasła!
Sesja wygasła!
Sesja wygasła!

Znaleziono wyników: 1

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On the Erdős–Dushnik–Miller theorem without AC

Banerjee Amitayu, Gopaulsingh Alexa

Bulletin of the Polish Academy of Sciences. Mathematics

2023

Vol. 71, no 1

1--21

In ZFA (Zermelo–Fraenkel set theory with the Axiom of Extensionality weakened to allow the existence of atoms), we prove that the strength of the proposition EDM (“If G = (VG,EG) is a graph such that VG is uncountable, then for every coloring f : [VG]2 → {0, 1} either there is an uncountable set monochromatic in color 0, or there is a countably infinite set monochromatic in color 1”) is strictly between DCN1 (where DCN1 is Dependent Choices for N1, a weak choice form stronger than Dependent Choices (DC)) and Kurepa’s principle (“Any partially ordered set such that all of its antichains are finite and all of its chains are countable is countable”). Among other new results, we study the relations of EDM to BPI (Boolean Prime Ideal Theorem), RT (Ramsey’s theorem), De Bruijn–Erdős’ theorem for n-colorings, König’s lemma and several other weak choice forms. Moreover, we answer a part of a question raised by Lajos Soukup.