Infinite Ordered Sets, A Recursive Perspective

摘要: This work surveys the development of theory infinite ordered sets along lines suggested by recursion theory. Since is principally concerned with explicit effective constructions, this line research retains much character mathematics finite sets. There are two distinct categories into which results fall: first individual on ordering can be mechanically determined, while second concerns whether elementary sentences true in a given class distinguished an algorithm. Roughly, sentence one that refers to elements set rather than, say, elements. “Width 3” notion expressible sentence, but “finite width” cannot expressed even such sentences. The requisite background and logic found Barwise [1977].