This question is inspired by the excellent question by Douglas Ulrich When is $L$-Rank definable in inner models of $V=L$? Suppose $M \in L$ is a countable model of $ZFC$, and fur …

Hi all! Is there anything like Gödel's constructible universe for New Foundations? More precisely, I would like a process for taking a model $M$ of NF, and using it to build a mod …

Everything I know on this subject comes from Sacks book : "Higher recursion theory" Let $\mathcal{O^Y}$ be the set of codes for ordinals constructive in $Y$. We should have the r …

I would like an example of a J-structure $(J^A,B)$ which is not acceptable and one that is not 1-sound. Edit:Let us recall that a structure $J^A_\alpha$ is acceptable if for every …

For $n$ a natural number, $\alpha$ an ordinal, let $p(n,\alpha)$ be the $n$-th projectum of $J_\alpha$, where $J$ is the Jensen hierarchy for $L$. Call a finite sequence $s:=(x_1 …