In mathematical logic, abstract model theory is a generalization of model theory that studies the general properties of extensions of first-order logic and their models. [1]
Abstract model theory provides an approach that allows us to step back and study a wide range of logics and their relationships. [2] The starting point for the study of abstract models, which resulted in good examples was Lindström's theorem. [3]
In 1974 Jon Barwise provided an axiomatization of abstract model theory. [4]
See also
References
- ^ Institution-independent model theory by Răzvan Diaconescu 2008 ISBN 3-7643-8707-6 page 3
- ^ Handbook of mathematical logic by Jon Barwise 1989 ISBN 0-444-86388-5 page 45
- ^ Jean-Yves Béziau Logica universalis: towards a general theory of logic 2005 ISBN 978-3-7643-7259-0 pages 20–25
- ^ J. Barwise, 1974 "Axioms for abstract model theory", Annals of Mathematical Logic 7:221–265
Further reading
- Jon Barwise; Solomon Feferman (1985). Model-theoretic logics. Springer-Verlag. ISBN 978-0-387-90936-3.
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| Logics |
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Formal systems (
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| Proof theory | |||||||||
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 | This mathematical logic-related article is a stub. You can help Wikipedia by expanding it. |
In mathematical logic, abstract model theory is a generalization of model theory that studies the general properties of extensions of first-order logic and their models. [1]
Abstract model theory provides an approach that allows us to step back and study a wide range of logics and their relationships. [2] The starting point for the study of abstract models, which resulted in good examples was Lindström's theorem. [3]
In 1974 Jon Barwise provided an axiomatization of abstract model theory. [4]
See also
References
- ^ Institution-independent model theory by Răzvan Diaconescu 2008 ISBN 3-7643-8707-6 page 3
- ^ Handbook of mathematical logic by Jon Barwise 1989 ISBN 0-444-86388-5 page 45
- ^ Jean-Yves Béziau Logica universalis: towards a general theory of logic 2005 ISBN 978-3-7643-7259-0 pages 20–25
- ^ J. Barwise, 1974 "Axioms for abstract model theory", Annals of Mathematical Logic 7:221–265
Further reading
- Jon Barwise; Solomon Feferman (1985). Model-theoretic logics. Springer-Verlag. ISBN 978-0-387-90936-3.
| 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. |