In mathematical logic, an abstract logic is a formal system consisting of a class of sentences and a satisfaction relation with specific properties related to occurrence, expansion, isomorphism, renaming and quantification. [1]
Based on Lindström's characterization, first-order logic is, up to equivalence, the only abstract logic that is countably compact and has Löwenheim number ω. [2]
See also
- Abstract algebraic logic – Study of the algebraization of deductive systems, based on the Lindenbaum–Tarski algebra
- Abstract model theory
- Löwenheim number – smallest cardinal number for which a weak downward Löwenheim–Skolem theorem holds
- Lindström's theorem
- Universal logic – Subfield of logic that studies the features common to all logical systems
References
- ^ C. C. Chang and Jerome Keisler Model Theory, 1990 ISBN 0-444-88054-2 page 128
- ^ C. C. Chang and Jerome Keisler Model Theory, 1990 ISBN 0-444-88054-2 page 132
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 | This mathematical logic-related article is a stub. You can help Wikipedia by expanding it. |
In mathematical logic, an abstract logic is a formal system consisting of a class of sentences and a satisfaction relation with specific properties related to occurrence, expansion, isomorphism, renaming and quantification. [1]
Based on Lindström's characterization, first-order logic is, up to equivalence, the only abstract logic that is countably compact and has Löwenheim number ω. [2]
See also
- Abstract algebraic logic – Study of the algebraization of deductive systems, based on the Lindenbaum–Tarski algebra
- Abstract model theory
- Löwenheim number – smallest cardinal number for which a weak downward Löwenheim–Skolem theorem holds
- Lindström's theorem
- Universal logic – Subfield of logic that studies the features common to all logical systems
References
- ^ C. C. Chang and Jerome Keisler Model Theory, 1990 ISBN 0-444-88054-2 page 128
- ^ C. C. Chang and Jerome Keisler Model Theory, 1990 ISBN 0-444-88054-2 page 132
| General | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Theorems (
list) and paradoxes | |||||||||
| Logics |
| ||||||||
| Set theory |
| ||||||||
|
Formal systems (
list), language and syntax |
| ||||||||
| Proof theory | |||||||||
| Model theory | |||||||||
| Computability theory | |||||||||
| Related | |||||||||
|
| This mathematical logic-related article is a stub. You can help Wikipedia by expanding it. |