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16 relations: Algebraic definition, Algebraic sentence, Algebraic structure, Cartesian product, Category theory, Commutative ring, Elementary theory, Euclidean geometry, First-order logic, Free variables and bound variables, Functor, Jon Barwise, Mathematical logic, Morphism, Propositional calculus, William Lawvere.
Algebraic definition
In mathematical logic, an algebraic definition is one that can be given using only equations between terms with free variables.
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Algebraic sentence
In mathematical logic, an algebraic sentence is one that can be stated using only equations between terms with free variables.
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Algebraic structure
In mathematics, and more specifically in abstract algebra, an algebraic structure on a set A (called carrier set or underlying set) is a collection of finitary operations on A; the set A with this structure is also called an algebra.
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Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
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Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
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Commutative ring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.
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Elementary theory
In mathematical logic, an elementary theory is one that involves axioms using only finitary first-order logic, without reference to set theory or using any axioms which have consistency strength equal to set theory.
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Euclidean geometry
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
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First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
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Free variables and bound variables
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation that specifies places in an expression where substitution may take place.
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Functor
In mathematics, a functor is a map between categories.
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Jon Barwise
Kenneth Jon Barwise (June 29, 1942 – March 5, 2000) was an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
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Propositional calculus
Propositional calculus is a branch of logic.
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William Lawvere
Francis William Lawvere (born February 9, 1937) is a mathematician known for his work in category theory, topos theory and the philosophy of mathematics.
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