@article{Enayat_Łełyk_2024, title={Categoricity-like Properties in the First Order Realm}, volume={1}, url={https://riviste.fupress.net/index.php/jpm/article/view/2934}, DOI={10.36253/jpm-2934}, abstractNote={<div class="page" title="Page 79"> <div class="layoutArea"> <div class="column"> <p>By classical results of Dedekind and Zermelo, second order logic imposes categoricity features on Peano Arithmetic and Zermelo-Fraenkel set theory. However, we have known since Skolem’s anti-categoricity theorems that the first order formulations of Peano Arithmetic and Zermelo- Fraenkel set theory (i.e., PA and ZF) are not categorical. Here we investigate various categoricity-like properties (including tightness, solidity, and internal categoricity) that are exhibited by a distinguished class of first order theories that include PA and ZF, with the aim of understanding what is special about canonical foundational first order theories.</p> </div> </div> </div>}, journal={Journal for the Philosophy of Mathematics}, author={Enayat, Ali and Łełyk, Mateusz}, year={2024}, month={Sep.}, pages={63–98} }