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Post Closed as "Not suitable for this site" by Eric Wofsey, Stefan Kohl♦, abx, Andrés E. Caicedo, Emil Jeřábek
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Lehs
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ZF$ZF$ define membership by conditions demanding the existence of some constructable right-side-terms $M $ ($x \in M$). Is it meaningsful to ask for a categorical axiom system here? Shouldn't it be prooved, that any two relations $\epsilon$ and $\varepsilon$ which satisfying the axioms allways fullfill: $\forall x \forall M: x\epsilon M \Leftrightarrow x \varepsilon M$?

ZF define membership by conditions demanding the existence of some constructable right-side-terms $M $ ($x \in M$). Is it meaningsful to ask for a categorical axiom system here? Shouldn't it be prooved, that any two relations $\epsilon$ and $\varepsilon$ which satisfying the axioms allways fullfill: $\forall x \forall M: x\epsilon M \Leftrightarrow x \varepsilon M$?

$ZF$ define membership by conditions demanding the existence of some constructable right-side-terms $M $ ($x \in M$). Is it meaningsful to ask for a categorical axiom system here? Shouldn't it be prooved, that any two relations $\epsilon$ and $\varepsilon$ which satisfying the axioms allways fullfill: $\forall x \forall M: x\epsilon M \Leftrightarrow x \varepsilon M$?

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Lehs
Lehs
  • 862
  • 9
  • 17

Is any axiom system for sets categorical?

ZF define membership by conditions demanding the existence of some constructable right-side-terms $M $ ($x \in M$). Is it meaningsful to ask for a categorical axiom system here? Shouldn't it be prooved, that any two relations $\epsilon$ and $\varepsilon$ which satisfying the axioms allways fullfill: $\forall x \forall M: x\epsilon M \Leftrightarrow x \varepsilon M$?