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

Volume 176 / 2003

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


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 $.


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

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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image