Abstract
Within the framework of category theory, Cantor diagrams are introduced as the common structure of the self-reference constructions by Cantor, Russell, Richard, Gödel, Péter, Turing, Kleene, Tarski, according to the so-called Cantor diagonal method. Such diagrams consist not only of diagonal arrows but also of idempotent, identity and shift arrows. Cantor theorem states that no Cantor diagram is commutative. From this theorem, all the constructions above can be systematically retrieved. We do this by grouping them into two main classes: the class based on Cantor diagrams with a numerical shift function and the class based on Cantor diagrams with a Boolean shift function.
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Germano, G.M., Mazzanti, S. Cantor Diagrams: A Unifying Discussion of Self-Reference. Applied Categorical Structures 11, 313–336 (2003). https://doi.org/10.1023/A:1024447013739
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DOI: https://doi.org/10.1023/A:1024447013739