Mathematical Logic QuarterlyVolume 29, Issue 5 p. 289-312 Article THE COMPLETE EXTENSIONS OF THE MONADIC SECOND ORDER THEORY OF COUNTABLE ORDINALS† J. Richard Büchi, J. Richard Büchi Department Computer Sciences, Purdue University, West Lafayette, Indiana 47907 (U.S.A.)Search for more papers by this authorDirk Siefkes, Dirk Siefkes Technische Universität Berlin, Fachbereich Informatik (20), D-1000 Berlin 10 Franklinstr. 28/29Search for more papers by this author J. Richard Büchi, J. Richard Büchi Department Computer Sciences, Purdue University, West Lafayette, Indiana 47907 (U.S.A.)Search for more papers by this authorDirk Siefkes, Dirk Siefkes Technische Universität Berlin, Fachbereich Informatik (20), D-1000 Berlin 10 Franklinstr. 28/29Search for more papers by this author First published: 1983 https://doi.org/10.1002/malq.19830290502Citations: 1 † Editor's note. The present paper by J. R. BÜCHI and D. SIEFKES and the two following ones by J. R. BÜCHI and CH. ZAIONTZ were written in 1972-1974, containing material from 1971 and 1972. For reasons beyond the authors' control they were not published. Since there has been much recent progress in the area, and the problem of the decidability of the monadic theory of ω2 is (in a certain sense) settled by the results of Y. GUREVICH, M. MAGIDOR, and S. SHELAH [9], it seems appropriate to publish the three papers in their original form. The two papers on axiomatization might also stimulate work on the still unsolved problem of an axiom system for the monadic theory of two successors. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume29, Issue51983Pages 289-312 RelatedInformation