On iterated forcing for successors of regular cardinals

• Autorzy: Todd Eisworth
• Języki publikacji: EN

Abstrakty

EN

We investigate the problem of when ≤λ-support iterations of < λ-complete notions of forcing preserve λ⁺. We isolate a property- properness over diamonds-that implies λ⁺ is preserved and show that this property is preserved by λ-support iterations. Our condition is a relative of that presented by Rosłanowski and Shelah in [2]; it is not clear if the two conditions are equivalent. We close with an application of our technology by presenting a consistency result on uniformizing colorings of ladder systems on {δ < λ⁺: cf(δ) = λ} that complements a theorem of Shelah [4].

Kategorie tematyczne

• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 179
• Numer: 3
• Strony: 249-266

Daty

wydano

2003

Twórcy

autor

Todd Eisworth

• Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, U.S.A.

Identyfikatory

DOI

10.4064/fm179-3-4