Asaf Karagila

Realizing realizability results with symmetric extensions

J. L. Krivine developed a new method based on realizability to create new models of ZF where the axiom of choice fails. One of the main questions was whether or not the same results can be obtained in classical methods (i.e. forcing based methods). We show that it is indeed possible for two of the three results to be obtained by symmetric extensions (and recently Krivine showed that appealing to an abstract theorem of ZF, the third model can also be obtained as a symmetric extension).