Number systems with simplicity hiearchies: A generalization of Conway's theory of surreal numbers (Q2758056)
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scientific article; zbMATH DE number 1679329
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Number systems with simplicity hiearchies: A generalization of Conway's theory of surreal numbers |
scientific article; zbMATH DE number 1679329 |
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5 July 2002
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surreal numbers
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simplicity hierarchy
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ordered field
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ordered group
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Number systems with simplicity hiearchies: A generalization of Conway's theory of surreal numbers (English)
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The surreal numbers form an ordered algebraic system that also possesses an ordered-tree structure (reflecting the recursive nature of the surreals). Moreover, these aspects of the surreals are connected to each other. This paper investigates other mathematical objects with similar properties and shows how such objects relate to the surreals. In particular, every divisible ordered abelian group (resp., real-closed field) is isomorphic to a subgroup (resp., subfield) of the surreals that is initial with respect to the tree structure.
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