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In math, a string is a sequence of symbols that are chosen from a set or alphabet. Formal languages are used in logic and in foundations of mathematics to represent the syntax of formal theories.
to work we need structure + axioms + logic = a theory?
(from Mathematical structure) In mathematics, a structure on a set, or more generally a type, consists of additional mathematical objects that in some manner attach (or are related) to the set, making it easier to visualize or work with, or endowing the collection with meaning or significance.
A partial list of possible structures are measures, algebraic structures (groups, fields, etc.), topologies, metric structures (geometries), orders, equivalence relations, and differential structures.