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On embedding models of arithmetic of cardinality ℵ₁ into reduced powers

Juliette Kennedy; Saharon Shelah — 2003

Fundamenta Mathematicae

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.

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