论文标题
自称理论
Self-referential theories
论文作者
论文摘要
我们以算术语言扩展了理论家庭的结构，使这些家庭可以彼此提及。如果理论包含表达自己的真理并表达特定的图灵指数的模式，并包含其他一些轻度的公理，那么该理论是不真实的。我们展示了一些真正的自称理论的家庭，这些家庭几乎无法避免这种禁止的模式。
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.
