theory of first-order theories, extensions by definitions formalize the introduction of new symbols by means of a definition. For example, it is common in...

In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They...

two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that...

things to which a property applies Extension (simplicial set) Extension by definitions Extensional definition, a definition that enumerates every individual...

which is concerned with whether the internal definitions of objects are the same. The extensional definition of function equality, discussed above, is commonly...

An enumerative definition of a concept or term is a special type of extensional definition that gives an explicit and exhaustive listing of all the objects...

theorem Galois extension Separable extension Normal extension Fraleigh (2014), Definition 31.1, p. 283. Malik, Mordeson, Sen (1997), Definition 21.1.23, p...

conservative extension of Zermelo–Fraenkel set theory with the axiom of choice ( Z F C {\displaystyle {\mathsf {ZFC}}} ). Extensions by definitions are conservative...

of f is X. In modern mathematical language, the domain is part of the definition of a function rather than a property of it. In the special case that X...

truth-conditional semantics.) Tarski developed the theory to give an inductive definition of truth as follows. (See T-schema) For a language L containing ¬ ("not")...

certain conditions with assurance that the extension will introduce no contradiction. Extension by definitions is perhaps the best-known approach, but it...

Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. Recursion is used in a variety of disciplines...

formats and devices. Specifically, this term defines an extension of the standard-definition television (SDTV) format that enables a clearer picture during...

There are two slightly different definitions of the term cyclotomic extension. It can mean either an extension formed by adjoining roots of unity to a field...

for Industrial and Applied Mathematics. pp. 16. ISBN 0-89871-420-6. "Definition of lemma | Dictionary.com". www.dictionary.com. Retrieved 2019-11-28....

finite abelian extension of local or global fields provides a quantitative measure of the ramification in the extension. The definition of the conductor...

left and right kan extensions. Spelling the definition of adjoints out, we get the following definitions; The right Kan extension amounts to finding the...

language Recursive language Recursion That is, under the Set-theoretic definition of natural numbers, the set of natural numbers less than a given natural...

particular without reference to set theory or using extensions such as plural quantification. Elementary definitions are of particular interest because they admit...

Yanchep Rail Extension. Enabling legislation was introduced to Parliament in May 2018 and passed in November 2018. The project definition plan, detailing...

Fallacies of definition are the various ways in which definitions can fail to explain terms. The phrase is used to suggest an analogy with an informal...

usage to see 'intension' used for both the composite and the primitive ideas. Extension Extensional definition Intension Intensional definition v t e...

adequately represented by the set of theorems alone. (For example, Kleene's logic has no theorems at all.) In such cases, alternative definitions of decidability...

stored in the file. The exact definition, giving the criteria for deciding what part of the file name is its extension, belongs to the rules of the specific...

{\displaystyle \aleph _{0},} the smallest infinite cardinality. The definition of ℵ 1 {\displaystyle \aleph _{1}} implies (in ZF, Zermelo–Fraenkel set...

(384–322 BCE) said definitions should describe the concept being defined in terms of other concepts already known. Mathematical proof was revolutionized by Euclid...

{\displaystyle \exists x\,(P(x)\wedge \forall y\,(P(y)\to y=x)).} An equivalent definition that separates the notions of existence and uniqueness into two clauses...

method and calling a method declared in the type definition. Not all languages implement extension methods in an equally safe manner, however. For instance...

more arguments in the form of independent variables designated in the definition, which can also contain parameters. The independent variables are mentioned...

attributes, viewed together by the mind, are seen under some connexion, that connexion is called a relation. — Augustus De Morgan Definition R is an n-ary relation...