PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Fundamenta Mathematicae

2016 | 234 | 1 | 15-40
Tytuł artykułu

### The linear refinement number and selection theory

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The linear refinement number 𝔩𝔯 is the minimal cardinality of a centered family in $[ω]^{ω}$ such that no linearly ordered set in $([ω]^{ω},⊆ *)$ refines this family. The linear excluded middle number 𝔩𝔵 is a variation of 𝔩𝔯. We show that these numbers estimate the critical cardinalities of a number of selective covering properties. We compare these numbers to the classical combinatorial cardinal characteristics of the continuum. We prove that 𝔩𝔯 = 𝔩𝔵 = 𝔡 in all models where the continuum is at most ℵ₂, and that the cofinality of 𝔩𝔯 is uncountable. Using the method of forcing, we show that 𝔩𝔯 and 𝔩𝔵 are not provably equal to 𝔡, and rule out several potential bounds on these numbers. Our results solve a number of open problems.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
15-40
Opis fizyczny
Daty
wydano
2016
Twórcy
autor
• Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland
• Department of Mathematics, Bar-Ilan University, Ramat Gan 5290002, Israel
autor
• Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 9190401 Jerusalem, Israel
• Mathematics Department, Rutgers University, New Brunswick, NJ, U.S.A.
autor
• Department of Mathematics, Bar-Ilan University, Ramat Gan 5290002, Israel
• Department of Mathematics, Weizmann Institute of Science, Rehovot 7610001, Israel
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory