Jamie Gabbay: An overview of my claimed proof of consistency of Quine's New Foundations скачать в хорошем качестве

Jamie Gabbay: An overview of my claimed proof of consistency of Quine's New Foundations

Heriot-Watt University http://gabbay.org.uk/ Abstract. NF is a mathematical foundation introduced in 1937 whose consistency remains an open problem. NF comes from a set theory tradition and is usually presented as a set theory with a universal set -- but it also admits a presentation as a type theory. Specifically, NF is closely related to the purely negative fragment of higher-order logic (meaning: having types of the form t ::= o | t \to o), and this is how I will present and work with it. I will describe the significance of ConNF and give a technical but accessible overview of my claimed proof of its consistency here https://arxiv.org/pdf/1406.4060.pdf The proof-method is based on standard techniques -- a concrete powersets model, a cut-admissibility argument, and then building a maximally consistent set -- though these are applied in a somewhat unusual way whose key points I will attempt to clearly describe. Questions and comments will be welcome.