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...

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

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

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...

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

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

x\,R\,y} and y S z {\displaystyle y\,S\,z} . This definition is a generalisation of the definition of functional composition. The defining properties...

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")...

logic, this is called an extension by definition (by equality) which is a conservative extension to a formal system. This is done by taking the equation defining...

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

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...

the definitions, first by length and then lexicographically. Now, we may map each definition to the set of natural numbers, such that the definition with...

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

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

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

valuation of extension over intension. See for example extension, and the extensional devices. Enumerative definition Extensional definition Extensional logic...

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...

for example by using the Łoś–Vaught test. Stating definitions and propositions in a way such that each new term can be formally eliminated by the priorly...

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

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...

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

worthy or fit' or 'that which commends itself as evident'. The precise definition varies across fields of study. In classic philosophy, an axiom is a statement...

the sentence. Description logic Connotation Extension (predicate logic) Extensionality Intensional definition Intensional logic Montague grammar Temperature...

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...

\exists !X(\operatorname {Union} (X,Y))} Then, one can use an extension by definition to add the union operator ⋃ A {\displaystyle \bigcup A} to the...

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

dictionary. Context as Other Minds Double entendre Extension Extensional definition Intension Intensional definition Loaded language Metacommunicative competence...