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The structure and development of mathematical theories. (English) Zbl 0746.03004

Summary: On the basis of a structural-naming reconstruction of scientific knowledge we give a description of the main subsystems of mathematical theories. The role of the theory of named sets for the exact analysis of their components is given. For the case of set theory we consider also some dynamic aspects.

MSC:

03A05 Philosophical and critical aspects of logic and foundations
00A30 Philosophy of mathematics
18C10 Theories (e.g., algebraic theories), structure, and semantics
18A15 Foundations, relations to logic and deductive systems
18B05 Categories of sets, characterizations
03-03 History of mathematical logic and foundations
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