Self-referential theories

Journal of Symbolic Logic 85 (4):1687-1716 (2020)
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We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing index for itself, and contains some other mild axioms, then that theory is untrue. We exhibit some families of true self-referential theories that barely avoid this forbidden pattern.

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Samuel Allen Alexander
Ohio State University (PhD)


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