urelement
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In set theory, a branch of mathematics, an urelement or ur-element (from the German prefix ur-, 'primordial') is an object that is not a set, but that may be an element of a set. It is also referred to as an atom or individual. Ur-elements are also not identical with the empty set.
~6 min read
Article
5 sectionsContents
- Theory
- Urelements in set theory
- Quine atoms<!--'Quine atom' and 'Reflexive set' redirect here-->
- References
- External links
In set theory, a branch of mathematics, an urelement or ur-element (from the German prefix ur-, 'primordial') is an object that is not a set, but that may be an element of a set. It is also referred to as an atom or individual. Ur-elements are also not identical with the empty set.
== Theory == There are several different but essentially equivalent ways to treat urelements in a first-order theory.
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semantic theory of truth
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set theory
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mathematical logic
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relation
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Peano axioms
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first-order logic
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formal system
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Zermelo–Fraenkel set theory
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recursive set
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semantics of logic
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von Neumann universe
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structure
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theory
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diagram
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non-well-founded set theory
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ground expression
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German
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mathematics
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universe
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