John U. Millar

This is one of the major products of the Scottish Enlightenment and a masterpiece of jurisprudence and social theory. Building on David Hume, Adam Smith, and their respective natural histories of man, John Millar developed a progressive account of the nature of authority in society by analysing changes in subsistence, agriculture, arts, and manufacture. 'The Origin of the Distinction of Ranks' is perhaps the most precise and compact development of the abiding themes of the liberal wing of the Scottish Enlightenment. Drawing on Smith's four-stages theory of history and the natural law's traditional division of domestic duties into those toward servants, children, and women, Millar provides a rich historical analysis of the ways in which progressive economic change transforms the nature of authority. In particular, he argues that, with the progress of arts and manufacture, authority tends to become less violent and concentrated, and ranks tend to diversify.

For countable structure, "Scott rank" provides a measure of internal, model-theoretic complexity. For a computable structure, the Scott rank is at most [Formula: see text]. There are familiar examples of computable structures of various computable ranks, and there is an old example of rank [Formula: see text]. In the present paper, we show that there is a computable structure of Scott rank [Formula: see text]. We give two different constructions. The first starts with an arithmetical example due to Makkai, and codes it into a computable structure. The second re-works Makkai's construction, incorporating an idea of Sacks.