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| Title Details: | |
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Godel's Incompleteness Theorems |
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| Authors: |
Koletsos, Georgios |
| Reviewer: |
Dimitrakopoulos, Konstantinos |
| Subject: | HUMANITIES AND ARTS > LOGIC AND PHILOSOPHY OF LOGIC HUMANITIES AND ARTS > LOGIC AND PHILOSOPHY OF LOGIC > LOGIC AND PHILOSOPHY OF LOGIC, MISCELLANEOUS > DEDUCTIVE LOGIC MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > MATHEMATICAL LOGIC AND FOUNDATIONS MATHEMATICS AND COMPUTER SCIENCE > COMPUTER SCIENCE |
| Description: | |
| Abstract: |
The Peano Arithmetic System. The arithmetic of Robinson. The concept of representability. Proof that all recursive functions are representable in arithmetic. Arithmetization of metamathematics. Proof that all metamathematical relations and functions are expressible with recursive relations and functions. Consistency and ω-consistency. Gödel's proof of the incompleteness of arithmetic. Extension of the proof through Rosser's theorem. Church-Turing undecidability results. Expressibility and Tarski's undefinability theorem for the truth predicate. Löb's theorem and related results. Proof of Gödel's second incompleteness theorem. Decidable and (essentially) undecidable theories.
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| Linguistic Editors: |
Toulatou, Dimitra |
| Technical Editors: |
Ksystra, Aikaterini |
| Type: |
Chapter |
| Creation Date: | 2015 |
| Item Details: | |
| License: |
http://creativecommons.org/licenses/by-nc-nd/3.0/gr |
| Handle | http://hdl.handle.net/11419/2304 |
| Bibliographic Reference: | Koletsos, G. (2015). Godel's Incompleteness Theorems [Chapter]. In Koletsos, G. 2015. Mathematical Logic [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/2304 |
| Language: |
Greek |
| Is Part of: |
Mathematical Logic |
| Publication Origin: |
Kallipos, Open Academic Editions |