Abstract:In this paper we present new ways to construct external subsets of nonstandard models of arithmetic using mostly internal sets, and show that if an ultraproduct of prime finite fields includes a copy of the algebraic real numbers then either this copy or its algebraic closure can be constructed in some of these ways. We also show that no copy of the field of real numbers inside such an ultraproduct can ever be constructed in any of these ways, but there is either a hyperreal field or an algebraically closed field of cardinality larger or equal to the continuum that can be.
| Comments: | Added a citation needed for a claim in the introduction |
| Subjects: | Logic (math.LO) |
| Cite as: | arXiv:2603.07508 [math.LO] |
| (or arXiv:2603.07508v4 [math.LO] for this version) | |
| https://doi.org/10.48550/arXiv.2603.07508 arXiv-issued DOI via DataCite |
From: Roee Sinai [view email]
[v1]
Sun, 8 Mar 2026 07:25:46 UTC (40 KB)
[v2]
Mon, 11 May 2026 15:29:19 UTC (40 KB)
[v3]
Thu, 21 May 2026 10:27:21 UTC (41 KB)
[v4]
Tue, 26 May 2026 14:30:34 UTC (41 KB)
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