Finite sets and Gödel's incompleteness theorems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Warszawa
Polska Akad. Nauk, Inst. Matematyczny
2003
|
| Schriftenreihe: | Dissertationes mathematicae
422 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 58, II S. |
Internformat
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Datensatz im Suchindex
| _version_ | 1804132784164306944 |
|---|---|
| adam_text | Titel: Finite sets and Gödel s incompleteness theorems
Autor: Świerczkowski, StanisłAw S
Jahr: 2003
CONTENTS
0. Introduction......................................................................................................................................................5
1. The language of HF and its coding..................................................... 6
2. T-fornmJas.......................................................................................................9
3. An flF-description of relations between formulas.........................................................11
d. The formula Pf................................................................................................................................................15
5. Phantom terms, functions and formulas................................................................................................18
G.GodePs First Incompleteness Theorem..................................................................................................21
7. Pseudo-coding..................................................................................................................................................23
8. The special p-function F................................................................29
O.Godcl s Second Incompleteness Theorem..............................................................................................31
10. Finite sets arid arithmetic..............................................................30
11. A theorem of Reinhardt................................................................37
Appendix: The axiomatic theory of finite sets..............................................40
1. Axioms and basic results........................................................................................................................41
2. Ordinals........................................................................................................................................................dd
3. p-functions..........................................................................d6
d. The rank function...................................................................d8
5. A definable order on the universe....................................................31
6. The standard model 6 of HF........................................................3d
References................................................................................................................................................................37
Abstract
We give complete proofs of the two famous incompleteness theorems of Godel. However, instead
of the usual choice of Peano Arithmetic, we take the theory of hereditarily finite sets as the basis
for the presentation.
2000 Mathematics Subject Classification: Primary 03F40; Secondary 03E30, 03E35.
Key words and phrases: hereditarily finite sets; coding; Godel s incompleteness theorems.
Research conducted while the author held the so-called Ulam Professorship at the University of
Colorado in Boulder.
Received 28.5.2003.
|
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| indexdate | 2024-07-09T19:58:19Z |
| institution | BVB |
| language | English |
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| physical | 58, II S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Polska Akad. Nauk, Inst. Matematyczny |
| record_format | marc |
| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae / Polska Akad. Nauk, Inst. Matematyczny |
| spelling | Swierczkowski, S. Verfasser aut Finite sets and Gödel's incompleteness theorems S. Świerczkowski Warszawa Polska Akad. Nauk, Inst. Matematyczny 2003 58, II S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae / Polska Akad. Nauk, Inst. Matematyczny 422 Gödel's theorem Incompleteness theorems Set theory Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd rswk-swf Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 s DE-604 Dissertationes mathematicae 422 (DE-604)BV000003039 422 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012817154&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Swierczkowski, S. Finite sets and Gödel's incompleteness theorems Dissertationes mathematicae Gödel's theorem Incompleteness theorems Set theory Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd |
| subject_GND | (DE-588)4021417-5 |
| title | Finite sets and Gödel's incompleteness theorems |
| title_auth | Finite sets and Gödel's incompleteness theorems |
| title_exact_search | Finite sets and Gödel's incompleteness theorems |
| title_full | Finite sets and Gödel's incompleteness theorems S. Świerczkowski |
| title_fullStr | Finite sets and Gödel's incompleteness theorems S. Świerczkowski |
| title_full_unstemmed | Finite sets and Gödel's incompleteness theorems S. Świerczkowski |
| title_short | Finite sets and Gödel's incompleteness theorems |
| title_sort | finite sets and godel s incompleteness theorems |
| topic | Gödel's theorem Incompleteness theorems Set theory Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd |
| topic_facet | Gödel's theorem Incompleteness theorems Set theory Gödelscher Unvollständigkeitssatz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012817154&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003039 |
| work_keys_str_mv | AT swierczkowskis finitesetsandgodelsincompletenesstheorems |