On embedding models of arithmetic of cardinality ℵ₁ into reduced powers

• Autorzy: Juliette Kennedy , Saharon Shelah
• Języki publikacji: EN

Abstrakty

EN

In the early 1970's S. Tennenbaum proved that all countable models of PA₁¯ + ∀₁ -Th(ℕ) are embeddable into the reduced product $ℕ^ω/ℱ$, where ℱ is the cofinite filter. In this paper we show that if M is a model of PA¯ + ∀₁ - Th(ℕ), and |M| = ℵ₁, then M is embeddable into $ℕ^ω/D$, where D is any regular filter on ω.

Kategorie tematyczne

• 03C20: Ultraproducts and related constructions
• 03C62: Models of arithmetic and set theory
• 03C50: Models with special properties (saturated, rigid, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 176
• Numer: 1
• Strony: 17-24

Daty

wydano

2003

Twórcy

autor

Juliette Kennedy

• Department of Mathematics, University of Helsinki, P.O. Box 4, FI-00014 University of Helsinki, Finland

autor

Saharon Shelah

• Institute of Mathematics, Hebrew University, 91904 Jerusalem, Israel,, Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, U.S.A.

Identyfikatory

DOI

10.4064/fm176-1-2