On the Use of Impredicative Reasoning to Construct a Class of Partial Models of ZF Within ZF: A mathematical paper by Bryan Ford. It claims that unless there's some error it follows from the exposition that ZF is inconsistent. The author is a researcher at MIT. This sensational remark is discreetly made in the conclusion. Abstract: "Goedel's incompleteness results show that if ZF is consistent, it is impossible to construct within ZF itself a single object (set) that represents a complete and precise semantic model of ZF. Nevertheless, it has also become clear since then that many kinds of partial models can be constructed within ZF that reveal interesting characteristics of ZF and related formal systems. We develop here one particular class of partial models of ZF, which rely on an extreme form of impredicative reasoning that nevertheless follow the accepted rules of set theory and first-order logic and are constructible within exactly the same variant of ZF as the one being modelled. Some study of these partial models yields interesting results." Link
monochrom is an art-technology-philosophy group having its seat in Vienna and Zeta Draconis. monochrom is an unpeculiar mixture of proto-aesthetic fringe work, pop attitude, subcultural science, context hacking and political activism. Our mission is conducted everywhere, but first and foremost in culture-archeological digs into the seats (and pockets) of ideology and entertainment. monochrom has existed in this (and almost every other) form since 1993. [more]
