# Questions tagged [nonstandard-analysis]

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.

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### Can nonstandard fields contain $\mathbb R$ in different ways?

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### Cofinality of infinitesimals

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### Influence of cardinal characteristics on nonstandard analysis?

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### Continuum hypothesis in nonstandard universe

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### Ultrapower of amenable group

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### Countable roots of unity

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### How to construct “inaccessible hypernatural”?

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### Embedding standard function spaces into superstructure

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### Self homomorphisms of hyperreals fixing the reals

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### Reference Request: A definition of topology using monads (a.k.a. halos)

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### Bertoglio&Chuaqui's nonstandard (discrete) proof of the Jordan curve theorem

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### Has anything (other than what is in the obituary witten by M. Noether) survived of Paul Gordan's defense of infinitesimals?

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### What is the Turing degree associated with an ultrafilter $U$?

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### What is $\mu$-approximablity in Loeb measure (conflicting statements in books)?

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### Turing degree of a turing machine with access to an (arbitrary) nonstandard integer

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### Was Cauchy prescient?

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### Non standard extension of real numbers via nonprincipal ultra filters

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### Did Bishop make those comments in his oral presentation?

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### Are the definable hyper-reals, using quantifiers only over the standard reals and natural numbers, the same as the algebraic numbers?

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### Automorphisms of the hyperreals over the rationals and nontrivial automorphism groups

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### How is compactness related to countable saturation?

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### Archimedean completeness of some fields

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### Compactness and omega models

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### What are the minimal requirements for the definable hyperreal field plus transfer?

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### Is there a model of ZF+ACC where transfer fails for the definable hyperreals?

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### Transfer with minimal choice

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### Can there be a numerical system in which logarithms can be expressed in terms of exponentials in closed form?

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### What's Reeb's take on naive integers?

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### Who said “the naive counting numbers don't exhaust $\Bbb N$”?

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### What is the modern consensus on the difficulty of infinitesimals?

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### What is… A Grossone? [closed]

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### What are the advantages of the more abstract approaches to nonstandard analysis?

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### Bibliographic request concerning an article by Bernstein and Robinson

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### Pontryagin dual of the surreal numbers?

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### “Lebesgue-measurable” cardinals and real-closed fields

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### Non-standard numbers and exponential form of Zeta function [closed]

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### Are there any standard analysis facts that can be proven or arrived only by means of non-archimedean extensions of reals and non-standard analysis?

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### Obtaining graphics of functions in non-standard analysis [closed]

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### Are hyperreal numbers isomorphic to formal power series?

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### Which universities teach true infinitesimal calculus? [closed]

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### Is non-existence of the hyperreals consistent with ZF?

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### Salvaging Leibnizian formalism?

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### Literature that helps explain what the theory of numerosities contributes with

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### Berkovich Analytification of the transseries

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### Survey of the history of calculus?

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### More information on Kruskal's treatment of Surreal numbers as an asymptotic behavior of a real valued function

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### Is a model of arithmetic contained in a model of arithmetic an initial segment?

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### Surreal numbers, ultrapowers of $\Bbb R$, ordinal-valued functions and the slow-growing hierarchy

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### Is there a source linking Robinson's work in wing theory with his theory of infinitesimals?

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