Excerpt from A Decision Procedure for Set-Theoretic Formulae Involving Rank and Cardinality Comparison The decidability of the extension of mls with the singleton operator, the cardinality operator together with arithmetic addition, subtraction and comparison was proved in [fosso]. Also, the decidability of mls extended with the singleton operator and the rank comparison predicate was established in [ccf88]. This paper extends and unifies both such results. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.