Constructions by transfinitely many workers
Julia F. Knight · Annals of Pure and Applied Logic · 1990
In one of the author's earlier articles the main result is a metatheorem for constructions by finitely many workers. In an article of Ash. Jokusch and Knight, there were two constructions which had, for an arbitrary recursive ordinal α, one worker for each β≤α. The present paper gives a metatheorem for constructions like these ones. The object of the construction is to produce: 1) a sequence of instructions with «labels» attached, following a prescribed «instruction function» that is recursive in 0 (α) , and 2) a recursive sequence of neighborhoods in a metric space, determining a point that «adheres» to the sequence of labels. The metatheorem is applied to pairs of structures