# 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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### Is anything known about $\Delta_n$ bounding?

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### Can $\mathsf{RCA}_0$ prove that every nonempty c.e. set $A \subseteq \mathbb{N}$ has a least element?

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### Legitimacy of the shadow map serving as a field homomorphism for a specific hyperfinite field formed of a union of hyperfine lattices

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### What's the size of non standard monad for weak topology?

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### Request for bibliographic information

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### Loeb measures and non-standard hull of Banach spaces

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### Decidability of a first-order theory of hyperreals

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### Unbounded $\omega_1$-sequence in $^*\mathbb{N}$

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### Isomorphism of hyperreal fields viewed as extensions of the field of reals

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

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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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### 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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