• Re: 2020-01-07

    From Mikko@21:1/5 to Ross Finlayson on Sun Dec 17 10:18:33 2023
    On 2023-12-16 18:26:39 +0000, Ross Finlayson said:

    If you count the axiom schema of separation as just one instead of a schema, ZF definitely is finitely axiomatized. (Also the other schemas have finite versions, i.e. their statements about filling the entire space of the higher-order.)

    Goedel's results are about finitely axiomatized theories.

    Gödel's incompleteness theorem (and related results) only require
    that there is a finite procedure that can determine whether a
    sentence is an axiom or not. It is not necessary that they can
    be expressed with a finite number of schemas.

    Mikko

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