nullane de tantis gregibus tibi digna videtur? rara avis in terra nigroque simillima cygno. Juvenal Sat. VI 161, 165. 1966-JNC visits AN at CornelI. An idea emerges. 1968-JNC is at V. c. L. A. for the Logic Year. The Los Angeles ma- script appears. 1970-AN visits JNC at Monash. 1971-The Australian manuscript appears. 1972-JNC visits AN at Cornell. Here is the result. We gratefully acknowledge support from Cornell Vniversity, Vni versity of California at Los Angeles, Monash Vniversity and National Science Foundation Grants GP 14363, 22719 and 28169. We are deeply indebted to the many people who have helped uso Amongst the mathe maticians, we are particularly grateful to J. C. E. Dekker, John Myhill, Erik Ellentuck, Peter AczeI, Chris Ash, Charlotte ehell, Ed Eisenberg, Dave Gillam, Bill Gross, Alan Hamilton, Louise Hay, Georg Kreisel, Phil Lavori, Ray Liggett, Al Manaster, Michael D. Morley, Joe Rosen stein, Graham Sainsbury, Bob Soare and Michael Venning. Last, but by no means least, we thank Anne-Marie Vandenberg, Esther Monroe, Arletta Havlik, Dolores Pendell, and Cathy Stevens and the girls of the Mathematics Department of VCLA in 1968 for hours and hours of excellent typing. Thanksgiving November 1972 J. N. Crossley Ithaca, New Y ork Anil Nerode Contents O. Introduction . . . . . . . 1 Part 1. Categories and Functors 3 1. Categories . . . . . . . . 3 2. Morphism Combinatorial Functors 3 3. Combinatorial Functors . . . . . 18 Part H. Model Theory . . 18 4. Countable Atomic Models 18 5. Copying . 22 6. Dimension . . . . . . . 26 Part III.

Inhalt
0. Introduction.- I. Categories and Functors.- 1. Categories.- 2. Morphism Combinatorial Functors.- 3. Combinatorial Functors.- II. Model Theory.- 4. Countable Atomic Models.- 5. Copying.- 6. Dimension.- III. Combinatorial Functions.- 7. Strict Combinatorial Functors.- 8. Strict Combinatorial Functions.- IV. Recursive Equivalence.- 9. Suitable Categories.- 10. Bridge.- 11. Recursive Equivalence (Sets).- 12. Recursive Equivalence (Linear Orderings).- 13. Recursive Equivalence in a General Setting.- 14. Existence of Dedekind Types.- 15. Partial Recursive Combinatorial Functors.- 16. Partial Recursive Strict Combinatorial Functors.- V. Identities.- 17. The Strong Topology.- 18. Extending Identities to Dedekind Dense Types.- 19. More on Identities.- 20. Uniform Implications for Dedekind Types.- VI. Frames.- 21. Frames.- 22. Frame Maps are Map Frames.- 23. Recursive Frame Maps are Recursive Map Frames.- 24. Chains and Chain Types.- 25. Extending Relations Using Frames.- VII. The Dimension Case.- 26. Extensions of Solutions of Equations.- 27. Universal Horn Sentences.- 28. Universal Sentences I.- 29. Universal Sentences II.- VIII. Sound Values.- 30. Soundly Based Types.- 31. Extending Partial Functions to Soundly Based Types.- 32. Functions from Infinite Dedekind Types to Soundly Based Dedekind Types.- 33. Total Functions to Soundly Based Dedekind Types.- IX. The Automorphism Extension Property.- 34. The Automorphism Extension Property.- 35. Regressive Types and Tree Frames.- 36. Solutions of Equations and the Automorphism Extension Property.- X. Satisfiability.- 37. Finitary Relations.- 38. The Master Frame.- 39. Satisfiability.- 40. Compactness and Dimension.- Index of Notations.- General Index.