In
mathematical logic
Mathematical logic is the study of Logic#Formal logic, 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 com ...
, an algebraic definition is one that can be given using only equations between terms with
free variables. Inequalities and quantifiers are specifically disallowed.
Saying that a definition is algebraic is a stronger condition than saying it is
elementary.
Related
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Algebraic theory
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Algebraic expression
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Algebraic equation
In mathematics, an algebraic equation or polynomial equation is an equation of the form P = 0, where ''P'' is a polynomial with coefficients in some field, often the field of the rational numbers.
For example, x^5-3x+1=0 is an algebraic equati ...
References
Mathematical logic
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