ICHD classification and diagnosis of migraine are further subdivided. Overall ICHD-3 beta distinguishes 29 migraine subtypes. The following table outlines the main subtypes and their ICHD-1, -2, -3 beta and ICD-10 codes. Migraine without aura also referred to as a "common migraine", (previously known as "hemicrania simplex") is a specific neurological disorder characterized by recurrent, throbbing headaches that often affect one side of the head (i.e., it is unilateral), are of at least moderate intensity, and may cause nausea, phonophobia or photophobia. One defining characteristic of the common migraine is a lack of the visual disturbances known as an aura. The exact International Classification of Headache
Formally real field properties are equivalent. It is also easy to see that a field that admits an ordering must satisfy these three properties. A proof that if "F" satisfies these three properties, then "F" admits an ordering uses the notion of and positive cones. Suppose −1 is not a sum of squares, then a Zorn's Lemma argument shows that the prepositive cone of sums of squares can be extended to a positive cone . One uses this positive cone to define an ordering: if and only if belongs to "P". A formally real field with no formally real proper algebraic extension is