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By an extension process we understand a partial structure associated with an extension, that is a pair (A, F), where A is the partial structure, and F is the way we add new elements. An extension process may be discrete or continuous, according as the elements added are finite or infinite. In some cases elements may be added element-wise. We limit our study to extension processes where a limit (final) structure exists. In the element-wise extensions the process can be considered to be an ordered set, with inclusion as the relation among elements of the set. So an extension would look like the following:
A=A One very simple example of such an extension process is free extension in free geometries.
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