TY - BOOK ID - 50714059 TI - Foundations of analysis over surreal number fields PY - 1987 SN - 1281798053 9786611798055 0080872522 0444702261 PB - Amsterdam ; New York : New York, N.Y., U.S.A. : North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., DB - UniCat KW - Surreal numbers. KW - Algebraic fields. KW - Mathematical analysis. KW - 517.1 Mathematical analysis KW - Mathematical analysis KW - Algebraic number fields KW - Algebraic numbers KW - Fields, Algebraic KW - Algebra, Abstract KW - Algebraic number theory KW - Rings (Algebra) KW - Numbers, Surreal KW - Number theory KW - Algebraic fields KW - 517.1 KW - Surreal numbers UR - https://www.unicat.be/uniCat?func=search&query=sysid:50714059 AB - In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are d ER -