Symmetric extensions are a generalisation of forcing used to extend models of ZF. We will give an introduction to the technique of symmetric extensions and use them to prove results in ZF. Specifically, we will show that \(\omega_1\) can be inaccessible in ZF. We will finally examine weak compactness in ZF, as many weak compactness results which are equivalent in ZFC are not equivalent in ZF. These non equivalences can be shown explicitly at \(\omega_1\).
