Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Given an uncountable cardinal κ with $κ = κ^{<κ}$ and $2^{κ}$ regular, we show that there is a forcing that preserves cofinalities less than or equal to $2^{κ}$ and forces the existence of a well-order of H(κ⁺) that is definable over ⟨H(κ⁺),∈⟩ by a Σ₁-formula with parameters. This shows that, in contrast to the case "κ = ω", the existence of a locally definable well-order of H(κ⁺) of low complexity is consistent with failures of the GCH at κ. We also show that the forcing mentioned above introduces a Bernstein subset of $^{κ}κ$ that is definable over ⟨H(κ⁺),∈⟩ by a Δ₁-formula with parameters.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
221-236
Opis fizyczny
Daty
wydano
2014
Twórcy
autor
- School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom
autor
- Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm226-3-2