19 мар. 2022 г. · The axiom of regularity can be reasonably be taken as describing what kind of set the axioms are meant to be talking about, the “well-founded” ...

4 мар. 2016 г. · The original purpose of the axiom of regularity was to ban non-well-founded sets and/or to guarantee that you can assign an ordinal rank to each ...

11 февр. 2016 г. · The axiom of regularity also implies there is no cycle of membership. So A∈B∈C∈D∈A A ∈ B ∈ C ∈ D ∈ A does not happen.

9 апр. 2019 г. · The axiom of regularity can be reasonably be taken as describing what kind of set the axioms are meant to be talking about, ...

1 нояб. 2019 г. · No such set exists in a set-theoretical universe satisfying the axiom of regularity, of course. It can exist in other contexts.

6 нояб. 2022 г. · Among other things, the axiom of regularity does, indeed, imply that no set is an element of itself. So there is no set with the property that ...

16 мая 2024 г. · Epsilon induction requires the axiom of regularity. However I have seen claims that much of “normal mathematics” does not. Certainly, 1st year ...

16 сент. 2022 г. · It is entirely possible to have set theories without the Axiom of Regularity — which is what allows us to prove that no set is an element of ...

11 мая 2020 г. · The axiom of regularity states A∩{A,B}=∅ A ∩ { A , B } = ∅ or B∩{A,B}=∅ B ∩ { A , B } = ∅ .

The axiom of regularity is usually stated in a positive. Continue Reading. If you state the axiom of regularity (also called the axiom of foundation) in a way ...