Axiom: Axiom Schema of Replacement (Abraham Frankel, 1922)deleteeditadd to favorites[id:715]vote: last edited 19 min ago by bookofproofs If \(X\) is a set of a domain and each element of \(X\) can be replaced by an element of another domain, then \(X\) will be replaced by a new set \(Y\). \[(\forall (a\in X)~\exists b~\phi(a,b)) \Rightarrow (\exists~Y~\forall~b~(b\in Y \Leftrightarrow \exists (a\in X)~\phi(a,b))).\] References [656] Hoffmann, Dirk W.: “Grenzen der Mathematik - Eine Reise durch die Kerngebiete der mathematischen Logik”, Spektrum Akademischer Verlag, 2011 What follows from what?This is (experimental) work in progress - if you miss an axiom, a definition, a theorem or a proof, if you find any inconsistencies you want to correct, or just know about a cool example or explanation you want to share with others, then join our team and help to improve this catalogue. Learn more about the axiomatic approach on BoP...Contribute to BoP: add a new Corollary add add a new Definition add add a new Motivation add add a new Example add add a new Application add add a new Explanation add add a new Interpretation add add a new Comment (Branch) add |
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