The monadic theory of order

Abstract

We deal with the monadic (second-order) theory of order. We prove all known results in a unified way, show a general way of reduction, prove more results and show the limitation on extending them. We prove (CH) that the monadic theory of the real order is undecidable. Our methods are model-theoretic, and we do not use automaton theory. This is a slightly corrected version of a very old work.