A Rather Classless Model
Matt Kaufmann · Proceedings of the American Mathematical Society · 1977
Using ${\diamondsuit _{{\omega _1}}}$, a model $\mathfrak {N}$ of Peano arithmetic is constructed which has a unique extension $(\mathfrak {N},\chi )$ to a model of $\Delta _1^1$-PA, Peano arithmetic with $\Delta _1^1$-comprehension.