Foundational Studies (eBook)

Lev D. Beklemishev (Autor)

eBook Download: PDF

2000 | 1. Auflage
604 Seiten
Elsevier Science (Verlag)
978-0-08-095501-8 (ISBN)

Infos

Provability, Computability and Reflection

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Foundational Studies

Inhalt

Front Cover 1
Foundational Studies: Selected Works 4
Copyright Page 5
Contents 6
Editorial note 8
Chapter 1. Countable Boolean fields and their application to general metamathematics 10
Chapter 2. On the independence of definitions of finiteness in a system of logic 27
Chapter 3. On some universal relations 77
Chapter 4. On the independence of the axiom of choice and some of its consequences 79
Chapter 5. Boolean rings with an ordered basis 84
Chapter 6. Axiom of choice for finite sets 101
Chapter 7. On absolute properties of relations 133
Chapter 8. On the principle of dependent choices 143
Chapter 9. Proofs of non-deducibility in intuitionistic functional calculus 147
Chapter 10. On a set of integers not definable by means of one-quantifier predicates 151
Chapter 11. Arithmetical classes and types of well ordered systems 157
Chapter 12. On the rules of proof in the pure functional calculus of the first order 158
Chapter 13. A classification of logical systems 163
Chapter 14. On models of axiomatic systems 201
Chapter 15. On direct products of theories 227
Chapter 16. On a system of axioms which has no recursively enumerable arithmetic model 258
Chapter 17. A lemma concerning recursive functions and its applications 264
Chapter 18. A formula with no recursively enumerable mode1 268
Chapter 19. Examples of sets definable by means of two and three quantifiers 284
Chapter 20. Contributions to the theory of definable sets and functions 296
Chapter 21. A proof of Herbrand’s theorem 301
Chapter 22. A generalization of a theorem of M. Deuring 307
Chapter 23. Concerning a problem of H. Scholz 315
Chapter 24. On a generalization of quantifiers 320
Chapter 25. On computable sequences 345
Chapter 26. On recursive models of formalized arithmetic 360
Chapter 27. On a problem of W. Kinna and K. Wagner 366
Chapter 28. On various degrees of constructivism 368
Chapter 29. A generalization of the incompleteness theorem 385
Chapter 30. An example of a non-axiomatizable many valued logic 413
Chapter 31. Concerning the problem of axiomatizability of the field of real numbers in the weak second order logic 418
Chapter 32. Definability of sets in models of axiomatic theories 436
Chapter 33. A compact space of models of first order theories 441
Chapter 34. An addition to the paper “A proof of Herbrand’s theorem” 446
Chapter 35. Axiomatizability of some many valued predicate calculi 451
Chapter 36. Representability of sets in formal systems 477
Chapter 37. A problem in the theory of models 497
Chapter 38. The Hilbert epsilon function in many-valued logics 503
Chapter 39. On models of Zermelo–Fraenkel set theory satisfying the axiom of constructibility 523
Chapter 40. Models of second order arithmetic with definable Skolem functions 550
Chapter 41. A transfinite sequence of .-models 563
Chapter 42. Partial orderings of the family of .-models 570
Chapter 43. A contribution to teratology 586
Chapter 44. A remark on models of the Gödel–Bernays axioms for set theory 599

Produkt-Details

• Erscheint lt. Verlag: 1.4.2000
• Sprache: englisch
• Themenwelt: Informatik ► Software Entwicklung ► User Interfaces (HCI)
• Themenwelt: Informatik ► Theorie / Studium ► Algorithmen
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik
• ISBN-10: 0-08-095501-0 / 0080955010
• ISBN-13: 978-0-08-095501-8 / 9780080955018