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In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables.. What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics for these deductive systems) and connected ...
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power.
Mathematical logic is the study of formal logic within mathematics. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. Mathematical logic is divided into four parts: Model theory; Proof theory; Recursion theory, also known as computability theory ...
Each of these outlines focuses on a mathematics or logic. Along with Wikipedia:Contents/Outlines, the outlines on Wikipedia form an all-encompassing outline of the knowledge of humankind. Pages included here should also be included in Category:Outlines.
Algebra • Algebraic structures • Reciprocity laws • Cohomology theories Calculus and analysis • Integrals • Mathematical series • Vector spaces Geometry and topology • Geometric shapes • Algebraic surfaces • Points Logic • First-order theories • Large cardinal properties • Paradoxes Number theory • Prime numbers
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.
An algebraic theory consists of a collection of n-ary functional terms with additional rules (axioms).. For example, the theory of groups is an algebraic theory because it has three functional terms: a binary operation a × b, a nullary operation 1 (neutral element), and a unary operation x ↦ x −1 with the rules of associativity, neutrality and inverses respectively.
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