Structures and Their Cryptomorphic Manifestations: Searching for Inquiry Tools (Algebraic System, Logic, Language and Related Areas in Computer Science)

Abstract

The search for the concept of a structure independent from the particular context of its application has a long history going back to the attempt made by Bourbaki more than a half century ago, but there is still no answer to the general question "What is a structure?" It is no wonder that the parallel question about the defrnition of cryptomorphism (understood as much more general concept than Birkhoffs cryptoisomorphism) has not been answered. The answer to one question can open a way to the other, as the group of cryptomorphisms should produce the corresponding structure as its invariant. The present paper considers tools for the inquiry in both directions of a structure and of a cryptomorphism.