To complement Andreas's answer (and perhaps Joel's forthcoming answer) let me plug Aczel's Anti-Foundation Axiom. This axiom says that every suitable "dots and arrows" diagram (as described by Hans) determines a unique set. It is thus a convenient way to generate a unique suitable set of urelements elements for just about any type of abstract structure than one wants to define. For more on this axiom, I recommend reading Aczel's Non-Well-Founded Sets (MR0940014) which can be found here.
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To complement Andreas's answer (and perhaps Joel's forthcoming answer) let me plug Aczel's Anti-Foundation Axiom. This axiom says that every suitable "dots and arrows" diagram (as described by Hans) determines a unique set. It is thus a convenient way to generate a unique suitable set of urelements for just about any type of abstract structure than one wants to define. For more on this axiom, I recommend reading Aczel's Non-Well-Founded Sets (MR0940014) which can be found here. |
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To complement Andreas's answer (and perhaps Joel's forthcoming answer) let me plug Aczel's Anti-Foundation Axiom. This axiom says that every suitable "dots and arrows" diagram (as described by Hans) determines a unique set. It is thus a convenient way to generate a unique suitable set of urelements for just about any type of abstract structure than one wants to define. For more on this axiom, I recommend reading Aczel's Non-Well-Founded Sets (MR0940014) which can be found here. |
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