Existence of a Precise axiomatization of Eudoxus theory of magnitude

68 Views Asked by At

Is there a precise axiomatization of the Eudoxus theory of proportions? For example,

a) (D, +, <) is a structure such that < is a strict linear order,

b) + is an order-preserving commutative and associative operation which is order-preserving,

c) for every x there is y such that nx =y,

d) Eudoxus-Archimede Axiom,

e) Continuity axiom …