Recursive surreal numbers.
نویسندگان
چکیده
منابع مشابه
Recursive definitions on surreal numbers
Let No be Conway’s class of surreal numbers. I will make explicit the notion of a function f on No recursively defined over some family of functions. Under some ‘tameness’ and uniformity conditions, f must satisfy some interesting properties; in particular, the supremum of the class ̆ x ∈ No : f (x) ≥ 0 ̄ is actually an element of No. As an application, I will prove that concatenation function x ...
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An open problem posed by John H. Conway in [2] was whether one could, on his system of numbers and games, ' . . . define operations of addition and multiplication which will restrict on the ordinals to give their usual operations'. Such a definition for addition was later given in [4], and this paper will show that a definition also exists for multiplication. An ordinal exponentiation operation...
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We show that the natural embedding of the differential field of transseries into Conway’s field of surreal numbers with the Berarducci-Mantova derivation is an elementary embedding. We also prove that any Hardy field embeds into the field of surreals with the Berarducci-Mantova derivation.
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In his monograph [Gon86], H. Gonshor showed that Conway’s real closed field of surreal numbers carries an exponential and logarithmic map. Subsequently, L. van den Dries and P. Ehrlich showed in [vdDE01] that it is a model of the elementary theory of the field of real numbers with the exponential function. In this paper, we give a complete description of the exponential equivalence classes (see...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1990
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093635498