# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## On embedding models of arithmetic of cardinality $\aleph _1$ into reduced powers

### Tom 176 / 2003

Fundamenta Mathematicae 176 (2003), 17-24 MSC: 03C62, 03C20, 03C50. DOI: 10.4064/fm176-1-2

#### Streszczenie

In the early 1970's S. Tennenbaum proved that all countable models of ${\rm PA}^- + \forall _1 -{\rm Th}({\mathbb N})$ are embeddable into the reduced product ${\mathbb N}^\omega /{\cal F}$, where ${\cal F}$ is the cofinite filter. In this paper we show that if $M$ is a model of ${\rm PA}^- + \forall _1 -{\rm Th}({\mathbb N})$, and $|M|=\aleph _1$, then $M$ is embeddable into ${\mathbb N}^\omega /D$, where $D$ is any regular filter on $\omega$.

#### Autorzy

• Juliette KennedyDepartment of Mathematics
University of Helsinki
P.O. Box 4
FI-00014 University of Helsinki
Finland
e-mail
• Saharon ShelahInstitute of Mathematics
Hebrew University
91904 Jerusalem, Israel

Department of Mathematics
Rutgers University
New Brunswick, NJ 08903, U.S.A.
e-mail

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