On embedding models of arithmetic of cardinality aleph₁ into reduced powers

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In the early 1970's S.Tennenbaum proved that all countable models of PA- + forall₁-Th(N) are embeddable into the reduced product Nᵒmega/F, where F is the cofinite filter. In this paper we show that if M is a model of PA- + forall₁-Th(N), and |M|= aleph₁, then M is embeddable into Nᵒmega/D, where D is any regular filter on omega.