${\Sigma }_1(\kappa )$-definable subsets of $\mathrm{H}({\kappa }^{+})$

Philipp Lücke, Ralf Schindler, Philipp Schlicht

We study ${\Sigma }_1({\omega }_1)$-definable sets (i.e. sets that are equal to the collection of all sets satisfying a certain ${\Sigma }_1$-formula with parameter ${\omega }_1$) in the presence of large cardina…