On embedding models of arithmetic of cardinality א1 into reduced powers

Juliette Kennedy; Saharon Shelah

doi:10.4064/fm176-1-2

On embedding models of arithmetic of cardinality א₁ into reduced powers

Juliette Kennedy^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In the early 1970's S. Tennenbaum proved that all countable models of PA^- + ∀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.

Original language	English
Pages (from-to)	17-24
Number of pages	8
Journal	Fundamenta Mathematicae
Volume	176
Issue number	1
DOIs	https://doi.org/10.4064/fm176-1-2
State	Published - 2003

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abstract = "In the early 1970's S. Tennenbaum proved that all countable models of PA- + ∀1 - Th(ℕ) are embeddable into the reduced product ℕω/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 Nω/D, where D is any regular filter on ω.",

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AB - In the early 1970's S. Tennenbaum proved that all countable models of PA- + ∀1 - Th(ℕ) are embeddable into the reduced product ℕω/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 Nω/D, where D is any regular filter on ω.

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On embedding models of arithmetic of cardinality א₁ into reduced powers

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