Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York
Springer
1981
|
| Schriftenreihe: | Lecture notes in mathematics
897 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | v, 383 Seiten |
| ISBN: | 3540111700 0387111700 |
Internformat
MARC
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| 245 | 1 | 0 | |a Iterated inductive definitions and subsystems of analysis |b recent proof-theoretical studies |c Wilfried Buchholz ; Solomon Feferman ; Wolfram Pohlers ; Wilfried Sieg |
| 264 | 1 | |a Berlin ; Heidelberg ; New York |b Springer |c 1981 | |
| 300 | |a v, 383 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 897 | |
| 650 | 4 | |a Analyse mathématique - Fondements | |
| 650 | 7 | |a Analyse mathématique - Fondements |2 ram | |
| 650 | 4 | |a Induction (Mathématiques) | |
| 650 | 7 | |a Induction (Mathématiques) |2 ram | |
| 650 | 4 | |a Preuve, Théorie de la | |
| 650 | 7 | |a Preuve, théorie de la |2 ram | |
| 650 | 4 | |a Induction (Mathematics) | |
| 650 | 4 | |a Mathematical analysis |x Foundations | |
| 650 | 4 | |a Proof theory | |
| 650 | 0 | 7 | |a Beweistheorie |0 (DE-588)4145177-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Induktive Definition |0 (DE-588)4161591-8 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |2 gnd-content | |
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| 689 | 1 | 1 | |a Beweistheorie |0 (DE-588)4145177-6 |D s |
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| 700 | 1 | |a Buchholz, Wilfried |d 1948- |0 (DE-588)143799738 |4 aut | |
| 700 | 1 | |a Feferman, Solomon |d 1928- |0 (DE-588)128682167 |4 aut | |
| 700 | 1 | |a Pohlers, Wolfram |d 1943- |0 (DE-588)1089378688 |4 aut | |
| 700 | 1 | |a Sieg, Wilfried |d 1945- |0 (DE-588)128682116 |4 aut | |
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| 830 | 0 | |a Lecture notes in mathematics |v 897 |w (DE-604)BV000676446 |9 897 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-001488474 | ||
Datensatz im Suchindex
| _version_ | 1804116722738790400 |
|---|---|
| adam_text | TABLE OF CONTENTS
Preface. How we got from there to here. (Feferman) 1
PART A. (USES OF) THEORIES OF INDUCTIVE DEFINITIONS.
Chapter I. Iterated inductive definitions and subsystems
of analysis. (Feferman, Sieg) 16
Introduction.
SI. Inductive definitions (on IN).
§1.1. General induction: operators, rule sets,
and games.
§1.2. Definable operators and their iteration.
§2. Formal theories for (parts of) classical
analysis.
§2.1. Theories for inductive definitions.
§2.2. Full classical analysis.
§2.3. Parts of classical analysis.
5 2.4. Reduction of ID systems to subsystems.
§3. Some proof theoretic methods and facts.
§3.1. Translations and partial truth definitions.
§3.2. Cut elimination for number theory and
ramified analysis.
§3.3. Iterated H. comprehension in ID systems.
Chapter II. Proof theoretic equivalences between classical
and constructive theories for analysis. (Feferman, Sieg) 78
Introduction.
SI. Reduction of subsystems of analysis to parts
of TQ.
§1.1. The system TQ; elementary facts.
§1.2. Subsystems related to the ramified hierarchy.
§1.3. Subsystems related to iterated inductive
definitions.
§2. Conservation results for theories with choice
and comprehension principles.
§2.1. The proof theoretic basis.
§2.2. Skolem operator theories for (Z +, AC)h.
§2.3. Infinitary operator theories for (I . AC).
Appendix (concerning two formulations of operator
IV
theories).
§3. Formal models for parts of T in analysis.
§3.1. (Refinements of) the set theoretic model.
§3.2. Recursion theoretic models.
§3.3. Final equivalences between subsystems of
analysis and of T .
PART B. PROOF THEORY OF THEORIES FOR INDUCTIVE DEFINITIONS
WITHOUT THE USE OF SPECIAL SYSTEMS OF ORDINAL NOTATIONS.
Chapter III. Inductive definitions, Constructive ordinals,
and normal derivations. (Sieg) 143
Introduction
51. Tree classes and infinitary logic.
11.1. The theory ID^ (JO for tree classes.
§1.2. Infinitary propositional logic PL^.
§2. Proof theory of PL .
§2.1. Hauptsatz and normal derivations.
§2.2. Embedding and MRP reduction.
§3. Conservation theorems.
§3.1. Presentation of syntax.
§3.2. Logical reflection.
Chapter IV. The fty,± rule. (Buchholz) 188
Introduction to the first part of Chapter IV.
§1. The formal theory ID~.
§2. The infinitary system ID°°.
§3. Majorization of deductions by abstract trees.
§4. Lower bounds for |ID1{ ) |
Introduction to the second part of Chapter IV.
§5. Reduction of ID~ to a strictly positive ID1 (00.
§6. Realizability of strictly positive ID^ (01)
V
PART C. PROOF THEORY OF THEORIES FOR INDUCTIVE DEFINITIONS
REQUIRING THE USE OF THE NOTATION SYSTEM (Q).
Chapter V. Ordinal analysis of IDy. (Buchholz) 234
Introduction.
§1. The functions q
a
§2. Majorization of abstract trees by ordinals.
§3. Constructive wellordering proofs.
Chapter VI. Proof theoretical analysis of IDV by the
method of local predicativity. (Pohlers) 261
Introduction.
§a. More about ordinal notations; the intro¬
duction of the collapsing functions.
§6. The infinitary system!*.
§61. The extended language LlJt (x,y,Xi) ieK
§62. The notion of proof for I*.
§63. Cut elimination for I*.
§64. Formalization in PA .
a
§Y. Conservative extension results.
§yl. Some provable formulas of I*.
§y2. Embedding of IDV into I*.
§y3. Formalization in PA .
a
§y4. Conservative extension results.
§y5. Further results.
§6. Characteristic ordinals for formal theories.
§61. Ordinal analysis for systems of iterated
inductive definitions and subsystems of analysis.
§62. The theory AUT(ID).
§63. The spectrum of a formal theory.
§64. More about the spectrum.
Bibliography. 358
Index. 369
|
| any_adam_object | 1 |
| author | Buchholz, Wilfried 1948- Feferman, Solomon 1928- Pohlers, Wolfram 1943- Sieg, Wilfried 1945- |
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| author_facet | Buchholz, Wilfried 1948- Feferman, Solomon 1928- Pohlers, Wolfram 1943- Sieg, Wilfried 1945- |
| author_role | aut aut aut aut |
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| isbn | 3540111700 0387111700 |
| language | English |
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| spelling | Iterated inductive definitions and subsystems of analysis recent proof-theoretical studies Wilfried Buchholz ; Solomon Feferman ; Wolfram Pohlers ; Wilfried Sieg Berlin ; Heidelberg ; New York Springer 1981 v, 383 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 897 Analyse mathématique - Fondements Analyse mathématique - Fondements ram Induction (Mathématiques) Induction (Mathématiques) ram Preuve, Théorie de la Preuve, théorie de la ram Induction (Mathematics) Mathematical analysis Foundations Proof theory Beweistheorie (DE-588)4145177-6 gnd rswk-swf Induktive Definition (DE-588)4161591-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Beweistheorie (DE-588)4145177-6 s DE-604 Induktive Definition (DE-588)4161591-8 s Buchholz, Wilfried 1948- (DE-588)143799738 aut Feferman, Solomon 1928- (DE-588)128682167 aut Pohlers, Wolfram 1943- (DE-588)1089378688 aut Sieg, Wilfried 1945- (DE-588)128682116 aut Erscheint auch als Online-Ausgabe 978-3-540-11170-2 Lecture notes in mathematics 897 (DE-604)BV000676446 897 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488474&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buchholz, Wilfried 1948- Feferman, Solomon 1928- Pohlers, Wolfram 1943- Sieg, Wilfried 1945- Iterated inductive definitions and subsystems of analysis recent proof-theoretical studies Lecture notes in mathematics Analyse mathématique - Fondements Analyse mathématique - Fondements ram Induction (Mathématiques) Induction (Mathématiques) ram Preuve, Théorie de la Preuve, théorie de la ram Induction (Mathematics) Mathematical analysis Foundations Proof theory Beweistheorie (DE-588)4145177-6 gnd Induktive Definition (DE-588)4161591-8 gnd |
| subject_GND | (DE-588)4145177-6 (DE-588)4161591-8 (DE-588)1071861417 |
| title | Iterated inductive definitions and subsystems of analysis recent proof-theoretical studies |
| title_auth | Iterated inductive definitions and subsystems of analysis recent proof-theoretical studies |
| title_exact_search | Iterated inductive definitions and subsystems of analysis recent proof-theoretical studies |
| title_full | Iterated inductive definitions and subsystems of analysis recent proof-theoretical studies Wilfried Buchholz ; Solomon Feferman ; Wolfram Pohlers ; Wilfried Sieg |
| title_fullStr | Iterated inductive definitions and subsystems of analysis recent proof-theoretical studies Wilfried Buchholz ; Solomon Feferman ; Wolfram Pohlers ; Wilfried Sieg |
| title_full_unstemmed | Iterated inductive definitions and subsystems of analysis recent proof-theoretical studies Wilfried Buchholz ; Solomon Feferman ; Wolfram Pohlers ; Wilfried Sieg |
| title_short | Iterated inductive definitions and subsystems of analysis |
| title_sort | iterated inductive definitions and subsystems of analysis recent proof theoretical studies |
| title_sub | recent proof-theoretical studies |
| topic | Analyse mathématique - Fondements Analyse mathématique - Fondements ram Induction (Mathématiques) Induction (Mathématiques) ram Preuve, Théorie de la Preuve, théorie de la ram Induction (Mathematics) Mathematical analysis Foundations Proof theory Beweistheorie (DE-588)4145177-6 gnd Induktive Definition (DE-588)4161591-8 gnd |
| topic_facet | Analyse mathématique - Fondements Induction (Mathématiques) Preuve, Théorie de la Preuve, théorie de la Induction (Mathematics) Mathematical analysis Foundations Proof theory Beweistheorie Induktive Definition Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488474&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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