A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points

Details A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points

2003-05-19

arxiv.org/abs/math/0305282v1

Mathematics

Logic

Scientific paper

Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses the semantic paradoxes, and how they arise as diagonal arguments and fixed point theorems in logic, computability theory, complexity theory and formal language theory.

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