Locally Σ₁-definable well-orders of H(κ⁺)

• Autorzy: Peter Holy , Philipp Lücke
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E35: Consistency and independence results
• 03E47: Other notions of set-theoretic definability

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 226
• Numer: 3
• Strony: 221-236

Daty

wydano

2014

Twórcy

autor

Peter Holy

• School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom

autor

Philipp Lücke

• Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany

Identyfikatory

DOI

10.4064/fm226-3-2