2020/08/11 by Alexander, Samuel Allen · 1 citation
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2008.11535
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.