The Monadic Theory of Order

Abstract

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