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Answer by Zhen Lin for What axioms need to be added to second-order ZFC...
My suggestion is essentially the same as Asaf's, but phrased a little differently to avoid directly mentioning inaccessible cardinals etc.A well-known way of making an axiomatisation of a structure...
View ArticleAnswer by Asaf Karagila for What axioms need to be added to second-order ZFC...
We already know that the models of $\sf ZFC_2$ are exactly the sets $V_\kappa$ for $\kappa$ inaccessible, so we really just want an axiom $\varphi$ such that $\sf ZFC_2+\varphi$ would only have one...
View ArticleWhat axioms need to be added to second-order ZFC before it has a unique model...
What axioms need to be added to ZFC2 (second-order ZFC) before the theory has a unique model (up to isomorphism)?I was thinking: adjoin the generalized continuum hypothesis (GCH) and a statement...
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