Fields of surreal numbers and exponentiation

• Autorzy: Lou van den Dries , Philip Ehrlich
• Języki publikacji: EN

Abstrakty

EN

We show that Conway's field of surreal numbers with its natural exponential function has the same elementary properties as the exponential field of real numbers. We obtain ordinal bounds on the length of products, reciprocals, exponentials and logarithms of surreal numbers in terms of the lengths of their inputs. It follows that the set of surreal numbers of length less than a given ordinal is a subfield of the field of all surreal numbers if and only if this ordinal is an ε-number. In that case, this field is even closed under surreal exponentiation, and is an elementary extension of the real exponential field.

Kategorie tematyczne

• 12J15: Ordered fields
• 03H05: Nonstandard models in mathematics
• 20F60: Ordered groups \SeeMainly{}
• 03C64: Model theory of ordered structures; o-minimality
• 03C65: Models of other mathematical theories

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 167
• Numer: 2
• Strony: 173-188

Daty

wydano

2001

Twórcy

autor

Lou van den Dries

• Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A.

autor

Philip Ehrlich

• Department of Philosophy, Ohio University, Athens, OH 45701, U.S.A.

Identyfikatory

DOI

10.4064/fm167-2-3