2010/05/06 by Rosinger, Elemer E.
#FOS: Mathematics #General Mathematics (math.GM)
paper · doi:10.48550/arxiv.1005.1243
Mathematical theories are classified in two distinct classes : \it rigid, and on the other hand, \it non-rigid ones. Rigid theories, like group theory, topology, category theory, etc., have a basic concept - given for instance by a set of axioms - from which all the other concepts are defined in a unique way. Non-rigid theories, like ring theory, certain general enough pseudo-topologies, etc., have a number of their concepts defined in a more free or relatively independent manner of one another, namely, with \it compatibility conditions between them only. As an example, it is shown that the usual ring structure on the integers ℤ is not rigid, however, it is nearly rigid.