CONTENTS -- Preface -- Organizing Committees -- Provably 02 and Weakly Descending Chains T. Arai -- 1. Introduction -- 2. Provably in -- 2.1. Infinitary derivations -- 2.2. Searching witnesses of Σ in derivations -- 2.3. Provably Σ -functions -- 3. Provably in EA -- A. Nested limit existence rules -- References -- Amalgamation, Absoluteness, and Categoricity J. Baldwin -- 1. The Universe is Wide or Deep -- 2. Abstract Elementary Classes -- 3. From L to First Order -- 4. The Conjecture for L -- 5. Absoluteness of Properties of Atomic Classes -- 6. Complexity -- 7. Conclusion -- 8. Appendix: Basic definability notions for L by David Marker -- References -- K-Trivials are Never Continuously Random G. Barmpalias, N. Greenberg, A. Montalb n and T. Slaman -- 1. Introduction -- 1.1. Randomness relative to continuous measures -- 1.2. K-triviality -- 1.3. Our results -- 2. K-trivial sets and NCR -- Action of requirement Rn -- 3. Incomplete r.e. degrees and NCR -- References -- Limitwise Monotonic Functions and Their Applications R. Downey, A. Kach and D. Turetsky -- 1. Introduction -- 2. Limitwise Monotonic Functions and Sets -- 3. Applications of Limitwise Monotonic Functions and Sets -- 4. Relativized Limitwise Monotonicity -- 5. Beyond Limitwise Monotonicity -- 6. Limitwise Monotonic Spectra -- 7. Open Questions -- References -- A Dichotomy for the Mackey Borel Structure I. Farah -- States -- 1. Proof of Theorem 1 -- 2. Concluding Remarks -- References -- On Automatic Families S. Jain, Y. Ong, Sh. Pu and F. Stephan -- 1. Introduction -- 2. The Size of Languages Inside a Family -- 3. Universal Complexity Measures -- 4. Characterising Automatic Families -- 5. Applications of Automatic Families in Learning Theory -- References -- Cappable CEA Sets and Ramsey's Theorem A. Kach, M. Lerman and R. Solomon -- 1. Introduction.

2. SRT and c-cappability -- The Construction -- References -- Computable Dowd-Type Generic Oracles M. Kumabe and T. Suzuki -- 1. Introduction -- 2. Notation -- 2.1. Strings and sets -- 2.2. Probability -- 2.3. Dowd-type generic oracles -- 3. Review of the Former Results -- 3.1. Review of our former paper -- 3.2. Comments on our former paper -- 4. The Case where r is Fixed -- 5. Proof of Main Theorem -- Acknowledgments -- References -- Models of Long Sentences I G. Sacks -- 1. Introduction -- 2. 1 Substructures -- 3. Akin to -Saturation -- 4. Proof of the Main Result -- 5. Extensions of MR and MR+ -- 5.1. The number of models -- 5.2. Atomic theories -- 5.3. L -- 6. Stability, Type-Completeness and Type-Admissibility -- References -- A Universally Free Modal Logic S. Yang -- 1. Some Presuppositions for a Na ve Metaphysical Conception of Modality and de re Constructions -- 2. A Syntactic Treatment of de re Constructions -- 3. The Underlying System IQ: A System of Universally Free Logic with Rigid Designators -- 4. A Quantified Modal System with Rigid Designators: A Natural Modal System IQS5 -- 5. A Modal System with Names as Constant Quantifiers -- References -- Author Index.