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Internal set

Index Internal set

In mathematical logic, in particular in model theory and non-standard analysis, an internal set is a set that is a member of a model. [1]

13 relations: Constructive non-standard analysis, Graduate Texts in Mathematics, Hyperreal number, Internal set theory, Mathematical logic, Model theory, Non-standard analysis, Robert Goldblatt, Standard part function, Transfer principle, Ultrafilter, Ultraproduct, Universe (mathematics).

Constructive non-standard analysis

In mathematics, constructive nonstandard analysis is a version of Abraham Robinson's non-standard analysis, developed by Moerdijk (1995), Palmgren (1998), Ruokolainen (2004).

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Graduate Texts in Mathematics

Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.

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Hyperreal number

The system of hyperreal numbers is a way of treating infinite and infinitesimal quantities.

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Internal set theory

Internal set theory (IST) is a mathematical theory of sets developed by Edward Nelson that provides an axiomatic basis for a portion of the non-standard analysis introduced by Abraham Robinson.

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Mathematical logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.

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Model theory

In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.

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Non-standard analysis

The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.

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Robert Goldblatt

Robert Ian Goldblatt (born 1949) is a mathematical logician at the School of Mathematics and Statistics at Victoria University, Wellington, New Zealand, and a member of the Centre for Logic, Language and Computation.

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Standard part function

In non-standard analysis, the standard part function is a function from the limited (finite) hyperreal numbers to the real numbers.

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Transfer principle

In model theory, a transfer principle states that all statements of some language that are true for some structure are true for another structure.

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Ultrafilter

In the mathematical field of set theory, an ultrafilter on a given partially ordered set (poset) P is a maximal filter on P, that is, a filter on P that cannot be enlarged.

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Ultraproduct

The ultraproduct is a mathematical construction that appears mainly in abstract algebra and in model theory, a branch of mathematical logic.

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Universe (mathematics)

In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains all the entities one wishes to consider in a given situation.

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Internal Set, Internal function.

References

[1] https://en.wikipedia.org/wiki/Internal_set

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