On embedding models of arithmetic of cardinality aleph_1 into reduced powers

Details On embedding models of arithmetic of cardinality aleph_1 into reduced powers On embedding models of arithmetic of cardinality aleph_1 into reduced powers

2001-05-16

arxiv.org/abs/math/0105134v1

Mathematics

Logic

Scientific paper

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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