wrote: " In ZFC for example the axiom of infinity is that anchor, but there is no initial model of PA in ZFC."
What do you mean by that last part? In ZFC we can define ω₀, the first countable ordinal, and make it into a model of PA using ordinal addition and multiplication. We can prove in ZFC that this is an initial segment of any model of PA in ZFC. We can prove in ZFC that it has a unique map of models into any model of PA in ZFC. So it's an initial model of PA in ZFC.
John Carlos Baez
npub1nf…3nqe4
2026-05-09 07:26:08 UTC
in reply to nevent1q…8e4w
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npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4Published at
2026-05-09 07:26:08 UTCEvent JSON
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"content": "wrote: \" In ZFC for example the axiom of infinity is that anchor, but there is no initial model of PA in ZFC.\"\n\nWhat do you mean by that last part? In ZFC we can define ω₀, the first countable ordinal, and make it into a model of PA using ordinal addition and multiplication. We can prove in ZFC that this is an initial segment of any model of PA in ZFC. We can prove in ZFC that it has a unique map of models into any model of PA in ZFC. So it's an initial model of PA in ZFC.",
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