On embedding models of arithmetic of cardinality $\aleph _1$
into reduced powers
Fundamenta Mathematicae, Tome 176 (2003) no. 1, pp. 17-24
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $.
Keywords:
early tennenbaum proved countable models forall mathbb embeddable reduced product mathbb omega cal where cal cofinite filter paper model forall mathbb aleph embeddable mathbb omega where regular filter omega
Affiliations des auteurs :
Juliette Kennedy 1 ; Saharon Shelah 2
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title = {On embedding models of arithmetic of cardinality $\aleph _1$
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Juliette Kennedy; Saharon Shelah. On embedding models of arithmetic of cardinality $\aleph _1$ into reduced powers. Fundamenta Mathematicae, Tome 176 (2003) no. 1, pp. 17-24. doi: 10.4064/fm176-1-2
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