On embedding models of arithmetic of cardinality $\aleph_1$ into reduced powers

by Kennedy and Shelah. [KeSh:728]
Fundamenta Math, 2003
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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