Is there a reliable, reasonably up-to-date, survey article doing a "compare and contrast" on varieties of non-standard analysis?
2026-03-29 03:28:25.1774754905
Survey of varieties of non-standard analysis?
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The best starting point is the detailed account by Hamkins here which will hopefully be published in a more formal venue eventually.
Two approaches that are not discussed there in detail are Hrbacek's relative set theory, as well as the $\alpha$-theory of Di Nasso and collaborators.
Also, the new edition of Nonstandard analysis for the working mathematician by Loeb and Wolff seems promising; see here. However I haven't been able to get my hands on a copy yet.
Such an article is online here, soon to appear in Real Analysis Exchange.