Preserving extension

In Logique mathematics, a logical theory T2 is a preserving extension of a theory T1 if the language of T2 extends the language of T1, if each theorem of T1 is a theorem of T2 and if any theorem of T2 which is in the language of T1 is already a theorem of T1.

Informellement, the new theory can possibly be more convenient to prove Théorème S, but it does not prove a new theorem concerning the old theory. The importance of this concept lies in the following theorem:

if T2 is a preserving extension of T1, and if T1 is coherent, then T2 is also coherent

Thus, the preserving extensions do not incur the risk to introduce new inconsistencies. They can also be seen like a Méthodologie to write and structure of the bulky theories: to start with a T0 theory known as coherent, and successively to build preserving extensions T1, T2, etc

The automatic Démonstrateur Isabelle adopts this methodology by providing a language for the preserving extensions by definition.

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