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Results tagged with nonstandard-analysis
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user 109573
Nonstandard analysis is a way of doing calculus and analysis with infinitesimals. The historical approach of Leibniz, Euler, and others to infinitesimal calculus was gradually replaced by epsilon, delta techniques in the context of a real continuum, in the 19th century. It was not until the 1960s that Abraham Robinson developed a theory of a hyperreal continuum that allows for a development of analysis procedurally akin to that of its founders.
10
votes
Do the surreal numbers enjoy the transfer principle in ZFC?
A partial answer to the focused question: it's not provable in ZFC that there is an OD class $\mathbb{Z}^*$ such that $(\mathbb{R}, +, \cdot, \mathbb{Z}) \equiv (\mathrm{No}, +, \cdot, \mathbb{Z}^*).$ …
- 4,316
3
votes
Surreals and NSA: some foundational issues
Problem 1: There is a definable proper class saturated real-closed field $\mathbb{R}^*$, defined by a slight modification of your and Shelah's construction, such that there is an $\mathrm{OD}_p$ injec …
- 4,316