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According to Wikipedia, the Goodstein's Theorem is provable from second order arithmetic, and since it implies Con(PA), PA can't prove it, assuming that PA is consistent. "Kirby and Paris showed that [Goodstein's Theorem] is unprovable in Peano arithmetic (but it can be proven in stronger systems, such as second-order arithmetic)."

According to Wikipedia, the Goodstein's Theorem is provable from second order arithmetic, and since it implies Con(PA), PA can't prove it, assuming that PA is consistent. "Kirby and Paris showed that [Goodstein's Theorem] is unprovable in Peano arithmetic (but it can be proven in stronger systems, such as second-order arithmetic)."

According to Wikipedia, Goodstein's Theorem is provable from second order arithmetic, and since it implies Con(PA), PA can't prove it, assuming that PA is consistent. "Kirby and Paris showed that [Goodstein's Theorem] is unprovable in Peano arithmetic (but it can be proven in stronger systems, such as second-order arithmetic)."

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  • 117
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According to Wikipedia, the Goodstein's Theorem is provable from second order arithmetic, and since it implies Con(PA), PA can't prove it, assuming that PA is consistent. "Kirby and Paris showed that [Goodstein's Theorem] is unprovable in Peano arithmetic (but it can be proven in stronger systems, such as second-order arithmetic)."