Fudan Logic Student Seminar 2025

March 20

Speaker: 陈俊宏 CHEN, Junhong

Time: 13:30 - 15:00. Location: HGW2403.

The Coding Conception of Set

This report focuses on a new Conception of Set developed in current research. This Conception takes ordinals as prior to sets and maintains that set theory ought to be regarded as a consequence of ordinal theory. Specifically, we argue that $\mathsf{ZFGC}$ is in fact a true first-order ordinal theory, while the true second-order ordinal theory admits three possible directions of divergence. Each of these directions offers a distinct prediction concerning the shape of the true set-theoretic universe: the $\mathsf{ZFGC}^2$ single universe, the countabilist single universe, and a new maximal single universe constructed from a multiverse perspective, which we refer to as the coding multiverse. By conducting technical derivations on the potential of the strengthened theories associated with these three possible directions, combined with philosophical arguments, we demonstrate that the third type of universe is sufficiently justified to be accepted, thereby proposing a new set-theoretic worldview. Finally, we briefly outline prospects for the possible Gödel Program within this worldview.