This will be a series of graduate lectures at Peking University, two lectures per week beginning mid-June and proceeding into July.
Topics. We shall aim to cover the central results in the modal logic of forcing, including an exploration of the main tools, and then explore how those ideas apply more generally in set-theoretic potentialism and other potentialist contexts, such as arithmetic potentialism and modal model theory. For prerequisites, students should be already familiar with some graduate-level set theory, including the basics of forcing, as well as standard tools from mathematical logic and model theory.
The lectures will focus on various research papers, as follows:
- Joel David Hamkins. “A simple maximality principle.” Journal of Symbolic Logic 68.2 (2003),pp. 527-550. doi:10.2178/jsl/1052669062. arXiv:math/0009240.
- Joel David Hamkins and Benedikt Löwe. “The modal logic of forcing.” Trans. AMS 360.4 (2008), pp. 1793-1817. doi:10.1090/S0002-9947-07-04297-3. arXiv:math/0509616.
- Joel David Hamkins and Øystein Linnebo. “The Modal Logic of Set-theoretic Potentialismand the Potentialist Maximality Principles.” Review of Symbolic Logic 15.1 (2022), pp. 1-35. doi:10.1017/S1755020318000242. arXiv:1708.01644.
- Joel David Hamkins and Wojciech Aleksander Wołoszyn. “Modal Model Theory.” Notre Dame Journal of Formal Logic 65.1 (2024), pp. 1-37. doi:10.1215/00294527-2024-0001.
- Joel David Hamkins and Øystein Linnebo. “Second-order Potentialism.” research manuscript in preparatoin.
- Joel David Hamkins. “The Modal Logic of Arithmetic Potentialism and the Universal Algorithm.” Philosophia Mathematica 34.1 (2026), pp. 137-182. doi:0.1093/philmat/nkag001.
- Joel David Hamkins. “Every countable model of arithmetic or set theory has a pointwise definable end extension.” Kriterion Journal of Philosophy (2024). doi:10.1515/krt-2023-0029. arXiv:2209.12578.
- Additional readings may be added, if time permits.