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- Internal_set abstract "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.The concept of internal sets is a tool in formulating the transfer principle, which concerns the logical relation between the properties of the real numbers R, and the properties of a larger field denoted *R called the hyperreal numbers. The field *R includes, in particular, infinitesimal (\"infinitely small\") numbers, providing a rigorous mathematical justification for their use. Roughly speaking, the idea is to express analysis over R in a suitable language of mathematical logic, and then point out that this language applies equally well to *R. This turns out to be possible because at the set-theoretic level, the propositions in such a language are interpreted to apply only to internal sets rather than to all sets (note that the term \"language\" is used in a loose sense in the above).Edward Nelson's internal set theory is an axiomatic approach to non-standard analysis (see also Palmgren at constructive non-standard analysis). Conventional infinitary accounts of non-standard analysis also use the concept of internal sets.".
- Internal_set wikiPageID "2190765".
- Internal_set wikiPageLength "2985".
- Internal_set wikiPageOutDegree "16".
- Internal_set wikiPageRevisionID "708355249".
- Internal_set wikiPageWikiLink Category:Non-standard_analysis.
- Internal_set wikiPageWikiLink Constructive_non-standard_analysis.
- Internal_set wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Internal_set wikiPageWikiLink Hyperreal_number.
- Internal_set wikiPageWikiLink Internal_set_theory.
- Internal_set wikiPageWikiLink Mathematical_logic.
- Internal_set wikiPageWikiLink Model_theory.
- Internal_set wikiPageWikiLink Non-standard_analysis.
- Internal_set wikiPageWikiLink Robert_Goldblatt.
- Internal_set wikiPageWikiLink Standard_part_function.
- Internal_set wikiPageWikiLink Transfer_principle.
- Internal_set wikiPageWikiLink Ultrafilter.
- Internal_set wikiPageWikiLink Ultraproduct.
- Internal_set wikiPageWikiLink Universe_(mathematics).
- Internal_set wikiPageWikiLinkText "Internal set".
- Internal_set wikiPageWikiLinkText "internal function".
- Internal_set wikiPageWikiLinkText "internal set".
- Internal_set wikiPageWikiLinkText "internal subset".
- Internal_set wikiPageUsesTemplate Template:Citation.
- Internal_set wikiPageUsesTemplate Template:Infinitesimals.
- Internal_set wikiPageUsesTemplate Template:Refimprove.
- Internal_set subject Category:Non-standard_analysis.
- Internal_set hypernym Member.
- Internal_set type Person.
- Internal_set type Field.
- Internal_set type Redirect.
- Internal_set comment "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.The concept of internal sets is a tool in formulating the transfer principle, which concerns the logical relation between the properties of the real numbers R, and the properties of a larger field denoted *R called the hyperreal numbers.".
- Internal_set label "Internal set".
- Internal_set sameAs Q6047933.
- Internal_set sameAs m.06tpy4.
- Internal_set sameAs Q6047933.
- Internal_set wasDerivedFrom Internal_set?oldid=708355249.
- Internal_set isPrimaryTopicOf Internal_set.