An introduction of variables into the frame of the basic theories for the foundations of mathematics (Q1335476)

Summary: We deal with the notion of a variable in the axiomatic frame of the basic theories for the Foundations of Mathematics [the authors, ibid. 5, No. 1, 11-22 (1994; Zbl 0797.03006)]. Variables are introduced into this frame as ``unary'' objects, taking values of different kinds, which can be connected by correlations (or correspondences), and allow local functional representations. In choosing the axioms on variables we take into account the main uses of the term ``variable'' in Mathematical Analysis, Mathematical Physics, Algebra, Geometry, Logic and in several exact and human sciences (Physics, Biology, Computer Science, Economics, Sociology, etc.).