Mathematical Logic: A structure for Zermelo Frankel Axioms

Asked Nov 24 '22 at 22:02

Active Nov 25 '22 at 07:49

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I have taken an interest in mathematical logic to understand to source of mathematics as we know it today. And in this regard I have the following two questions:

What would a logical structure/interpretation look like for the Zermelo-Frankel axioms?
How is it possible to define a logical structure if we don't know anything about functions or sets yet? To be clearer, objects like functions or sets follow from the Zermelo-Frankel axioms, but these objects are already used in the definitions of structures and interpretations before we even know that these objects exist.

asked Nov 24 '22 at 22:02

Tom

8

How is it possible to write a dictionary, if we don't know anything about words yet? – Gerry Myerson Nov 24 '22 at 22:06
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See https://mathoverflow.net/q/297942/1946. – JDH Nov 24 '22 at 22:38
I think there are also other much older questions, in the very early days of MO, addressing this issue. – JDH Nov 24 '22 at 23:04
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Here are some other related MO questions. Do set-theorists use informal set theory as their meta-theory when talking about models of ZFC? The sets in mathematical logic, Circular, or missing, definition in set theory? – Timothy Chow Nov 24 '22 at 23:06
See also the post What could be a model of ZFC? – Mauro ALLEGRANZA Nov 25 '22 at 14:17

Mathematical Logic: A structure for Zermelo Frankel Axioms

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