SZPILRAJN,ARROW AND SUZUMURA: CONCISE PROOFS OF EXTENSION THEOREMS AND AN EXTENSION

This paper extends the classical extension theorem established by Edward Szpilrajn (Fundamenta Mathematicae, 16, pp. 386–389, 1930). Szpilrajn's theorem states that every quasi‐ordering has an ordering extension. Because of its usefulness in various themes of economics, it has been applied by many researchers. Important generalizations have been presented by two authors, Kenneth Arrow and Kotaro Suzumura, among others. First, we provide concise proofs of four extension theorems by Szpilrajn, Arrow and Suzumura. We then show an extension of their extension theorems.