Abstract
AbstractOften philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power and meta-theoretic properties when comparing first-order and second-order logic.
Funder
Volkswagen Foundation
H2020 European Research Council
Universität Konstanz
Publisher
Springer Science and Business Media LLC
Reference18 articles.
1. Dutilh Novaes, C. (2019). Axiomatizations of arithmetic and the first-order/second-order divide. Synthese, 196(7), 2583–2597.
2. Ebbinghaus, H.-D., Flum, J., & Thomas, W. (1996). Einführung in die Mathematische Logik. Berlin: Spektrum Akademischer. 4. Auflage.
3. Hamkins, J.D., & Yang, R. (2013). Satisfaction is not absolute. arXiv:1312.0670v1 [math.LO].
4. Hintikka, J. (1989). Is there completeness in mathematics after gödel? Philosophical Topics, 17(2), 69–90.
5. Kennedy, J., Magidor, M., & Väänänen, J. (2021). Inner models from extended logics: Part 1. Journal of Mathematical Logic, 21(2), 2150012.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献