Gödel's Incompleteness theorems:
This Element takes a deep dive into Gödel's 1931 paper giving the first presentation of the Incompleteness Theorems, opening up completely passages in it that might possibly puzzle the student, such as the mysterious footnote 48a. It considers the main ingredients of Gödel's proof: arith...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2022
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| Schlagworte: | |
| Online-Zugang: | BSB01 UBG01 Volltext |
| Zusammenfassung: | This Element takes a deep dive into Gödel's 1931 paper giving the first presentation of the Incompleteness Theorems, opening up completely passages in it that might possibly puzzle the student, such as the mysterious footnote 48a. It considers the main ingredients of Gödel's proof: arithmetization, strong representability, and the Fixed Point Theorem in a layered fashion, returning to their various aspects: semantic, syntactic, computational, philosophical and mathematical, as the topic arises. It samples some of the most important proofs of the Incompleteness Theorems, e.g. due to Kuratowski, Smullyan and Robinson, as well as newer proofs, also of other independent statements, due to H. Friedman, Weiermann and Paris-Harrington. It examines the question whether the incompleteness of e.g. Peano Arithmetic gives immediately the undecidability of the Entscheidungsproblem, as Kripke has recently argued. It considers set-theoretical incompleteness, and finally considers some of the philosophical consequences considered in the literature |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 06 Apr 2022) |
| Beschreibung: | 1 Online-Ressource (80 Seiten) |
| ISBN: | 9781108981972 |
| DOI: | 10.1017/9781108981972 |
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| spelling | Kennedy, Juliette 1955- (DE-588)1023532948 aut Gödel's Incompleteness theorems Juliette Kennedy Cambridge Cambridge University Press 2022 1 Online-Ressource (80 Seiten) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 06 Apr 2022) This Element takes a deep dive into Gödel's 1931 paper giving the first presentation of the Incompleteness Theorems, opening up completely passages in it that might possibly puzzle the student, such as the mysterious footnote 48a. It considers the main ingredients of Gödel's proof: arithmetization, strong representability, and the Fixed Point Theorem in a layered fashion, returning to their various aspects: semantic, syntactic, computational, philosophical and mathematical, as the topic arises. It samples some of the most important proofs of the Incompleteness Theorems, e.g. due to Kuratowski, Smullyan and Robinson, as well as newer proofs, also of other independent statements, due to H. Friedman, Weiermann and Paris-Harrington. It examines the question whether the incompleteness of e.g. Peano Arithmetic gives immediately the undecidability of the Entscheidungsproblem, as Kripke has recently argued. It considers set-theoretical incompleteness, and finally considers some of the philosophical consequences considered in the literature Gödel's theorem Incompleteness theorems Logic, Symbolic and mathematical Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd rswk-swf Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-108-98699-1 https://doi.org/10.1017/9781108981972 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kennedy, Juliette 1955- Gödel's Incompleteness theorems Gödel's theorem Incompleteness theorems Logic, Symbolic and mathematical Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd |
| subject_GND | (DE-588)4021417-5 |
| title | Gödel's Incompleteness theorems |
| title_auth | Gödel's Incompleteness theorems |
| title_exact_search | Gödel's Incompleteness theorems |
| title_exact_search_txtP | Gödel's Incompleteness theorems |
| title_full | Gödel's Incompleteness theorems Juliette Kennedy |
| title_fullStr | Gödel's Incompleteness theorems Juliette Kennedy |
| title_full_unstemmed | Gödel's Incompleteness theorems Juliette Kennedy |
| title_short | Gödel's Incompleteness theorems |
| title_sort | godel s incompleteness theorems |
| topic | Gödel's theorem Incompleteness theorems Logic, Symbolic and mathematical Gödelscher Unvollständigkeitssatz (DE-588)4021417-5 gnd |
| topic_facet | Gödel's theorem Incompleteness theorems Logic, Symbolic and mathematical Gödelscher Unvollständigkeitssatz |
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