Object language

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A language that is an object of study. In the formalization of a meaningful theory one distinguishes two languages. One is the language of the formalized theory, or the object language, given by the construction rules of expressions in the object language and by semantic rules, denoting what its expressions stand for or how they express a reasoning. The other is the language in which one formulates the syntactic and semantic rules mentioned above. This language is called a meta-language. Usually, a meta-language is not formalized. However, it can be formalized, and it then becomes an object language for whose study one needs a new meta-language.


[1] S.C. Kleene, "Introduction to metamathematics" , North-Holland (1951)
How to Cite This Entry:
Object language. V.N. Grishin (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098