In my Master's Thesis I want to show the following result by [Gitik, Moti (1980). All uncountable cardinals can be singular. Israel Journal of Mathematics, Vol. 35 no. 1-2, pp. 61-88.]: Assuming the consistency of arbitrarily large strongly compact cardinals, we show the consistency of 'ZF + all uncountable cardinals are singular'. To this end, we will start with a countable transitive model M of 'ZFC + there exist arbitrarily large strongly compact cardinals', force with a proper class forcing to get a model M[G] satisfying 'ZF - Power Set + Collection + all sets are countable', and finally define a symmetric submodel N_G, which will have the required properties.