Fields of surreal numbers and exponentiation (Q2717646)
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scientific article; zbMATH DE number 1605241
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fields of surreal numbers and exponentiation |
scientific article; zbMATH DE number 1605241 |
Statements
Fields of surreal numbers and exponentiation (English)
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17 June 2001
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surreal number
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exponential field
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The authors consider sets of the form: all surreal numbers whose length is less than a given ordinal. They show that the ordinal determines certain algebraic properties of the corresponding set. In particular, the set is a field iff the ordinal is an epsilon-number. Furthermore, such a field will be closed under exponentiation. The key lemmas establish bounds on the lengths of the surreals resulting from various algebraic operations.
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