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Mikhail Katz
Mikhail Katz
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user2529
user2529

I read with interest both Hamkins Multiverse Axioms and Joyal and Moerdijk's algebraic set theoryalgebraic set theory. Both of these perspectives takes a set-theory universe as an object, and consider collections of set-theory universes. The former lives in the setting of first-order logic, while the later lives in the setting of category theory (specifically monads and algebras).

Has there been an attempt to compare these theories? In particular (I hope the following is a well-founded question), does Hamkins' Multiverse axiomatize (the set-theory part, i.e. ignoring the intuitionistic and topos theoretic part) the class category of ZF-algebras?

I'm not too familiar with both these theories, but I have a great interest in Foundations. I would be thankful for more detailed comparisons beyond the particular question that I ask.

I read with interest both Hamkins Multiverse Axioms and Joyal and Moerdijk's algebraic set theory. Both of these perspectives takes a set-theory universe as an object, and consider collections of set-theory universes. The former lives in the setting of first-order logic, while the later lives in the setting of category theory (specifically monads and algebras).

Has there been an attempt to compare these theories? In particular (I hope the following is a well-founded question), does Hamkins' Multiverse axiomatize (the set-theory part, i.e. ignoring the intuitionistic and topos theoretic part) the class category of ZF-algebras?

I'm not too familiar with both these theories, but I have a great interest in Foundations. I would be thankful for more detailed comparisons beyond the particular question that I ask.

I read with interest both Hamkins Multiverse Axioms and Joyal and Moerdijk's algebraic set theory. Both of these perspectives takes a set-theory universe as an object, and consider collections of set-theory universes. The former lives in the setting of first-order logic, while the later lives in the setting of category theory (specifically monads and algebras).

Has there been an attempt to compare these theories? In particular (I hope the following is a well-founded question), does Hamkins' Multiverse axiomatize (the set-theory part, i.e. ignoring the intuitionistic and topos theoretic part) the class category of ZF-algebras?

I'm not too familiar with both these theories, but I have a great interest in Foundations. I would be thankful for more detailed comparisons beyond the particular question that I ask.

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user2529
user2529

Does the class category of ZF-algebras satisfy the Multiverse axioms?

I read with interest both Hamkins Multiverse Axioms and Joyal and Moerdijk's algebraic set theory. Both of these perspectives takes a set-theory universe as an object, and consider collections of set-theory universes. The former lives in the setting of first-order logic, while the later lives in the setting of category theory (specifically monads and algebras).

Has there been an attempt to compare these theories? In particular (I hope the following is a well-founded question), does Hamkins' Multiverse axiomatize (the set-theory part, i.e. ignoring the intuitionistic and topos theoretic part) the class category of ZF-algebras?

I'm not too familiar with both these theories, but I have a great interest in Foundations. I would be thankful for more detailed comparisons beyond the particular question that I ask.