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| Title Details: | |
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First-order predicate calculus |
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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 Language of First-Order Predicate Logic. Quantification. Free and bound variables. The concept of a proposition. Substitution of free variables by terms. Interpretation of the language. Tarski's definition of truth. Models of a set of propositions. Hilbert-type axiomatic systems. Theories with equality. Deduction theorems, constancy theorems, formal proofs of basic propositions. Complete theories, Lindenbaum's lemma, Henkin theories, proof of Gödel's completeness theorem. Extension of the theorem to theories with equality. Extension of the theorem to enumerable languages. Applications of the completeness theorem, the compactness theorem, Löwenheim-Skolem theorems. A brief introduction to Model Theory.
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| Linguistic Editors: |
Toulatou, Dimitra |
| Technical Editors: |
Stavrinos, Giorgos |
| Type: |
Chapter |
| Creation Date: | 2015 |
| Item Details: | |
| License: |
http://creativecommons.org/licenses/by-nc-nd/3.0/gr |
| Handle | http://hdl.handle.net/11419/2302 |
| Bibliographic Reference: | Koletsos, G. (2015). First-order predicate calculus [Chapter]. In Koletsos, G. 2015. Mathematical Logic [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/2302 |
| Language: |
Greek |
| Is Part of: |
Mathematical Logic |
| Publication Origin: |
Kallipos, Open Academic Editions |