Hilbert’s Axiom of (Arithmetic) Completeness first appeared in his classic investigation Über den Zahlbegriff (Hilbert 1900a, 183) as a novel means of distinguishing the ordered field R of real… (More)

In his monograph On Numbers and Games [1976], J. H. Conway introduced a realclosed field containing the reals and the ordinals as well as a great many less familiar numbers including -ω, ω/2, 1/ω, √ω… (More)

An R~-universally extending ordered field of power N, is constructed for each regular power N,, where 0 < of -< On and Zt~<~ 2• <-X,. When ,R, is inaccessible, the structure is either a (set) model… (More)

Introduction. In his monograph On Numbers and Games [7], J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many other numbers including -co, co/2,… (More)

Each surreal number has a unique Conway name (or normal form) that is characteristic of its individual properties. The paper answers the following two questions that are naturally suggested by the… (More)

In the decades bracketing the turn of the twentieth century the real number system was dubbed the arithmetic continuum because it was held that this number system is completely adequate for the… (More)

We examine the notions of negative, infinite and hotter than infinite temperatures and show how these unusual concepts gain legitimacy in quantum statistical mechanics. We ask if the existence of an… (More)