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By combining the methods of two former papers of ours ([6] and [7]) we develop a finitary ordinal analysis of the axiom system KPi of Kripke-P atek set theory with an inaccessible universe. As a main result we obtain an upper bound (in the fast-growing hierarchy) for the provably recursive functions of KPi. [ABSTRACT FROM AUTHOR]

Mathematical logic and foundations of mathematics experienced a large boom in the 1950s and 60s due to their close connections to the theoretical fundamentals of computer science. The theory of algorithms and automata developed in line with computer technology; cybernetics was the buzzword of the times. It was during this exciting period that G?nter Asser founded the Zeitschrift für Mathematische Logik und Grundlagen der Mathematik while doing his doctorate at the Humboldt-Universität in Berlin, together with his supervisor, Karl Schröter. The first issue appeared in 1955 and, alongside work by R. Péter and K. Schröter, contained a paper by Günter Asser entitled “Eine semantische Charakterisierung der deduktiv abgeschlossenen Mengen des Prädikatenkalküls der ersten Stufe”. Numerous further works would cement his status as a central figure in logic in East Germany as well as his international reputation. In 1960 Günter Asser was called to Greifswald University. He gave his students not merely a holistic view of the mathematical disciplines, but also of their history and philosophical background. As time went on, he became Dean of his faculty and Deputy Vice Chancellor (Prorektor) of the University. He went on to become a board member of the GDR Mathematical Society and, in 1977, was elected a member of the Academy of Science. His companion and mentor of many years, Karl Schröter, died that same year and Günter Asser assumed sole responsibility of the Zeitschrift für Mathematische Logik und Grundlagen der Mathematik. From a scientific viewpoint, the 70s were characterized by a tendency towards complexity theory. Günter Asser's influence was now mainly reflected in many publications from his field as well as in his opening up the journal to contributions on complexity theory. It is due to Günter Asser that the ZML, which in the meantime is called Mathematical Logic Quarterly, continues to enjoy such an eminent standing among the community, despite scientific and political paradigm shifts. As its editor, he ensured not only the high quality of the papers, but was also actively involved in the technical side of the journal's production. Günter Asser has accompanied the journal with his untiring, personal commitment for 50 years. We now wish to express our heartfelt thanks to the co-founder and retiring editor for his efforts on behalf of the journal, and wish him all the best for the future. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

A complete list of Finsler, Scott and Boffa sets whose transitive closures contain 1, 2 and 3 elements is given. An algorithm for deciding the identity of hereditarily finite Scott sets is presented. Anti-well-founded (awf) sets, i. e., non-well-founded sets whose all maximal ∈-paths are circular, are studied. For example they form transitive inner models of ZFC minus foundation and empty set, and they include uncountably many hereditarily finite awf sets. A complete list of Finsler and Boffa awf sets with 2 and 3 elements in their transitive closure is given. Next the existence of infinite descending ∈-sequences in Aczel universes is shown. Finally a theorem of Ballard and Hrbáček concerning nonstandard Boffa universes of sets is considerably extended. [ABSTRACT FROM AUTHOR]