Openly generated Boolean algebras and the Fodor-type reflection principle

• Autorzy: Sakaé Fuchino , Assaf Rinot
• Języki publikacji: EN

Abstrakty

EN

We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is ℵ₂-projective. Previously it was known that this characterization of openly generated Boolean algebras follows from Axiom R. Since FRP is preserved by c.c.c. generic extension, we conclude in particular that this characterization is consistent with any set-theoretic assertion forcable by a c.c.c. poset starting from a model of FRP. A crucial step of the proof of the main result is to show that FRP implies Shelah's Strong Hypothesis (SSH). In particular, we show that FRP implies the Singular Cardinals Hypothesis (SCH). Extending a result of the second author, we also establish some new characterizations of SSH in terms of topological reflection theorems.

Kategorie tematyczne

• 06E05: Structure theory
• 03E55: Large cardinals
• 03E65: Other hypotheses and axioms
• 03E75: Applications of set theory
• 03G05: Boolean algebras
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 212
• Numer: 3
• Strony: 261-283

Daty

wydano

2011

Twórcy

autor

Sakaé Fuchino

• Graduate School of System Informatics, Kobe University, Rokko-dai 1-1, Nada-ku, Kobe 657-8501, Japan

autor

Assaf Rinot

• Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Be'er Sheva, 84105 Israel

Identyfikatory

DOI

10.4064/fm212-3-4