Structure (mathematical logic)
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it. Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures with no relation symbols. In database theory, structures with no functions are studied as models for relational databases, in the form of relational models.
- Comment
- enIn universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it. Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures with no relation symbols. In database theory, structures with no functions are studied as models for relational databases, in the form of relational models.
- Date
- enNovember 2022
- Has abstract
- enIn universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it. Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures with no relation symbols. Model theory has a different scope that encompasses more arbitrary theories, including foundational structures such as models of set theory. From the model-theoretic point of view, structures are the objects used to define the semantics of first-order logic. For a given theory in model theory, a structure is called a model if it satisfies the defining axioms of that theory, although it is sometimes disambiguated as a semantic model when one discusses the notion in the more general setting of mathematical models. Logicians sometimes refer to structures as "interpretations", whereas the term "interpretation" generally has a different (although related) meaning in model theory, see interpretation (model theory). In database theory, structures with no functions are studied as models for relational databases, in the form of relational models.
- Is primary topic of
- Structure (mathematical logic)
- Label
- enStructure (mathematical logic)
- Link from a Wikipage to an external page
- plato.stanford.edu/entries/logic-classical/%234
- archive.org/details/courseinmodelthe0000poiz
- plato.stanford.edu/entries/logic-classical/
- www.math.uni-hamburg.de/home/diestel/books/graph.theory/
- archive.org/details/mathematicallogi1996ebbi
- archive.org/details/modeltheory0000hodg
- plato.stanford.edu
- www.thoralf.uwaterloo.ca/htdocs/ualg.html
- Link from a Wikipage to another Wikipage
- A K Peters
- Algebra
- Algebraic structure
- Algebra over a field
- Arity
- Bart Jacobs
- Bertrand Russell
- Cambridge University Press
- Categorical logic
- Category:Mathematical logic
- Category:Mathematical structures
- Category:Model theory
- Category:Universal algebra
- Category (mathematics)
- Category theory
- Complexity of constraint satisfaction
- Complex number
- Concrete category
- Conjunctive query
- Constraint satisfaction problem
- CRC Press
- Database
- Database theory
- Domain of discourse
- Elementary class
- Empty domain
- Fibred category
- Field (mathematics)
- Field extension
- Finitary
- Finitary closure operator
- Finitary relation
- Finite model theory
- First-order logic
- Foundations of mathematics
- Glossary of graph theory
- Graph (discrete mathematics)
- Graph homomorphism
- Graph theory
- Group (mathematics)
- Higher-order logic
- Injective function
- Integer
- Interpretation (logic)
- Interpretation (model theory)
- Join (mathematics)
- Lattice (order)
- Many-sorted logic
- Map (mathematics)
- Mathematical model
- Mathematical structure
- Meet (mathematics)
- Model theory
- Monomorphism
- Morphism (category theory)
- Natural number
- New York City
- Ordered field
- Power set
- Principia Mathematica
- Proper class
- Rational number
- Real number
- Relational model
- Relation symbol
- Ring (mathematics)
- Second-order logic
- Semantic model
- Set (mathematics)
- Set theory
- Signature (logic)
- Springer Science+Business Media
- Springer-Verlag
- Subcategory
- Subobject
- Subring
- Substructure (mathematics)
- Theory (mathematical logic)
- T-schema
- Type theory
- Universal algebra
- Variety (universal algebra)
- Vector space
- Zermelo–Fraenkel axioms
- Reason
- en"Interpretation" seems to be used with slightly different meanings in model theory versus other areas of mathematical logic, and to a beginner it is not necessarily entirely clear which sense is meant here. It appears to be the sense corresponding to "interpretation function" defined in the section below, but if so that is somewhat confusing, because the notion of "interpretation function" has not yet been defined in the article here yet is already being referenced. There may be a way to phrase this so that it is also clearer to beginners.
- SameAs
- Estructura (lógica)
- Estrutura de interpretação (lógica)
- m.0bfvql
- Model (logika)
- Model (matematik mantiq)
- Modello (logica matematica)
- nc6s
- Q1851710
- Structure (logique mathématique)
- Structure (mathematical logic)
- Struktur (erste Stufe)
- Struktur (logika matematika)
- מבנה (לוגיקה מתמטית)
- ساختار (منطق ریاضی)
- 结构 (数理逻辑)
- 구조 (논리학)
- SeeAlso
- Model theory
- Universal algebra
- Subject
- Category:Mathematical logic
- Category:Mathematical structures
- Category:Model theory
- Category:Universal algebra
- WasDerivedFrom
- Structure (mathematical logic)?oldid=1122738897&ns=0
- WikiPageLength
- 30953
- Wikipage page ID
- 4055928
- Wikipage revision ID
- 1122738897
- WikiPageUsesTemplate
- Template:All
- Template:Authority control
- Template:Citation
- Template:Citation needed
- Template:Clarification needed
- Template:Fact
- Template:Main
- Template:Mathematical logic
- Template:More footnotes
- Template:Reflist
- Template:See also
- Template:Short description
- Template:Visible anchor