KURT GÖDEL AND THE INCOMPLETENESS OF MODAL AXIOMATIC SYSTEMS
KURT GÖDEL AND THE INCOMPLETENESS OF MODAL AXIOMATIC SYSTEMS

Summary/Abstract: A fundamental contribution in the history of mathematical logic was the Kurt Gôdel’s theorem: if we have a predicative formalization of the simple domain of mathematics, arithmetic and build with these logical formulas an axiomatic system then is stranded every trial of building a completeness system, what it demonstrates as theorems all formulas what is valid in the arithmetical domain. The incompleteness what is the Gôdel’s discovery in the mathematical fields, is appeared, and, in the logical fields. We have discovered that the incompleteness is in the levels of modal logic.

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