Logic Seminar: Maria Beatrice Buonaguidi

Mathematically adequate and philosophically principled accounts of proper classes allowing for self-membership appear to be essential for investigations on the foundations of mathematics. Self-membered proper classes would be essential for a class theoretic foundation of category theory, and  principled accounts of proper classes can shed light on questions concerning the resolution of paradoxes of self-reference and the connection of class membership with related notions, such as property instantiation.

A possible way to obtain a mathematically adequate, philosophically principled theory of type-free classes is to extend theories of non-well-founded sets such as Aczel's (1988), and a starting point for this endeavour is the extension of Incurvati's (2014) graph conception of set to the class-theoretic domain. In this talk, I will set out to do so, presenting a conception of class called "the closed conception of class". I will informally present the conception and a class of natural models for it, the hyperuniverses of  Forti and Honsell (1989). Then, I will sketch a tentative axiomatisation for a theory of closed classes.

Peter Aczel. Non-Well-Founded Sets. Palo Alto, CA, USA: CSLI Lecture Notes, 1988.

Marco Forti and Furio Honsell. Models of self-descriptive set theories. Springer, 1989.

Luca Incurvati. The Graph Conception of Set. Journal of Philosophical Logic 43 (1):181-208, 2014.

Aula 1, Palazzetto Gorresio

 https://www.llc-philosophy.unito.it/logicllc/logicllc-seminars#h.p6jzvcednh77