Fundamental concept in metalogic, and the term may be used without qualification with differing meanings depending on the context within mathematical logic
Also known as syntactically complete · semantically complete · syntactical completeness · semantical completeness
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In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete. The term "complete" is also used without qualification, with differing meanings depending on the context, mostly referring to the property of semantic validity. Intuitively, a system is called complete in this particular sense, if it can derive every formula that is true.