In
mathematical logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...
, an algebraic sentence is one that can be stated using only equations between terms with
free variable
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not ...
s. Inequalities and quantifiers are specifically disallowed.
Sentential logic
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations b ...
is the subset of
first-order logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...
involving only algebraic sentences.
Saying that a sentence is algebraic is a stronger condition than saying it is
elementary
Elementary may refer to:
Arts, entertainment, and media Music
* ''Elementary'' (Cindy Morgan album), 2001
* ''Elementary'' (The End album), 2007
* ''Elementary'', a Melvin "Wah-Wah Watson" Ragin album, 1977
Other uses in arts, entertainment, a ...
.
Related
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Algebraic theory Informally in mathematical logic, an algebraic theory is a theory that uses axioms stated entirely in terms of equations between terms with free variables. Inequalities and quantifiers are specifically disallowed. Sentential logic is the subset o ...
*
Algebraic definition In mathematical logic, 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 ...
*
Algebraic expression In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations ( addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). ...
Mathematical logic
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