# 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. - published version (8p)

Bib entry

@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}, doi = {10.4064/fm176-1-2}, mrclass = {03C62 (03C20 03C50)}, mrnumber = {1971470}, doi = {10.4064/fm176-1-2}, note = {\href{https://arxiv.org/abs/math/0105134}{arXiv: math/0105134}}, arxiv_number = {math/0105134} }