On embedding models of arithmetic of cardinality ℵ₁ into reduced powers
Juliette Kennedy ; Saharon Shelah
Fundamenta Mathematicae, Tome 177 (2003), p. 17-24 / Harvested from The Polish Digital Mathematics Library
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In the early 1970’s S. Tennenbaum proved that all countable models of PA₁¯ + ∀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.

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:282915 
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     title = {On embedding models of arithmetic of cardinality 1 into reduced powers},
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     year = {2003},
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Juliette Kennedy; Saharon Shelah. On embedding models of arithmetic of cardinality ℵ₁ into reduced powers. Fundamenta Mathematicae, Tome 177 (2003) pp. 17-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm176-1-2/