Sh:728

• Kennedy, J. C., & Shelah, S. (2003). On embedding models of arithmetic of cardinality \aleph_1 into reduced powers. Fund. Math., 176(1), 17–24. arXiv: math/0105134 DOI: 10.4064/fm176-1-2 MR: 1971470
• Abstract:
  In the early 1970’s S.Tennenbaum proved that all countable models of PA^- + \forall_1 -Th({\mathbb N}) are embeddable into the reduced product {\mathbb N}^\omega/{\mathcal F}, where {\mathcal F} is the cofinite filter. In this paper we show that if M is a model of PA^- + \forall_1 -Th({\mathbb N}), and |M|=\aleph_1, then M is embeddable into {\mathbb N}^\omega/D, where D is any regular filter on \omega.
• Version 2001-05-09_11 (9p) published version (8p)

@article{Sh:728,
 author = {Kennedy, Juliette Cara and Shelah, Saharon},
 title = {{On embedding models of arithmetic of cardinality $\aleph_1$ into reduced powers}},
 journal = {Fund. Math.},
 fjournal = {Fundamenta Mathematicae},
 volume = {176},
 number = {1},
 year = {2003},
 pages = {17--24},
 issn = {0016-2736},
 mrnumber = {1971470},
 mrclass = {03C62 (03C20 03C50)},
 doi = {10.4064/fm176-1-2},
 note = {\href{https://arxiv.org/abs/math/0105134}{arXiv: math/0105134}},
 arxiv_number = {math/0105134}
}