### 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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