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On embedding models of arithmetic of cardinality aleph_1 into reduced powers

Juliette Kennedy·Saharon Shelah
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Abstract

In the early 1970's S.Tennenbaum proved that all countable models of PA^- + forall_1-Th(N) are embeddable into the reduced product N^omega/F, where F is the cofinite filter. In this paper we show that if M is a model of PA^- + forall_1-Th(N), and |M|= aleph_1, then M is embeddable into N^omega/D, where D is any regular filter on omega.

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Juliette Kennedy, Saharon Shelah. 2001-05-16. On embedding models of arithmetic of cardinality aleph_1 into reduced powers. https://arxiv.org/abs/math/0105134

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