Second-Order Reflection on Ordinals
Juan P. Aguilera
(ORCID: 0000-0002-2768-6714)
Disciplines
Mathematics (100%)
Keywords
- Inductive Definition,
- Kripke-Platek,
- Admissible Set,
- Reflecting Ordinal
Ordinal numbers are natural extensions of the counting numbers. They allow counting ordered collections of objects past infinity. As ordinal numbers grow bigger and bigger, they become harder and harder to describe precisely. This is made precise by the notion of reflection: large enough ordinal numbers cannot be defined by simple formulas. For many classes of formulas C, we can isolate the C-reflecting ordinals: the ordinals which cannot be described by formulas in C. The current project aims at identifying the smallest C-reflecting ordinals for various C and comparing their relative sizes.
Research institution(s)
- Technische Universität Wien - 100%
Project participants
- Vera Fischer, Universität Wien , mentor
International project participants
- Andreas Weiermann, Ghent University - Belgium
Research Output
- 12 Publications
- 1 Disseminations
- 2 Fundings
Publications
-
2025
Title Binary Choice Games and Arithmetical Comprehension DOI 10.48550/arxiv.2510.12612 Type Preprint Author Aguilera J Link Publication -
2025
Title The logic of correct models DOI 10.1142/s0219061325500047 Type Journal Article Author Aguilera J Journal Journal of Mathematical Logic -
2025
Title ON WINNING STRATEGIES FOR $F_\sigma $ GAMES DOI 10.1017/jsl.2024.77 Type Journal Article Author Aguilera J Journal The Journal of Symbolic Logic -
2026
Title Reflection properties of ordinals in generic extensions DOI 10.1016/j.apal.2026.103765 Type Journal Article Author Aguilera J Journal Annals of Pure and Applied Logic -
2026
Title Induction on dilators and Bachmann-Howard fixed points DOI 10.1016/j.apal.2026.103740 Type Journal Article Author Aguilera J Journal Annals of Pure and Applied Logic -
2025
Title The metamathematics of separated determinacy DOI 10.1007/s00222-025-01322-3 Type Journal Article Author Aguilera J Journal Inventiones mathematicae -
2023
Title Gödel-Dummett linear temporal logic Type Other Author Aguilera -
2023
Title Reflection Properties of Ordinals in Generic Extensions DOI 10.48550/arxiv.2311.12533 Type Preprint Author Aguilera J -
2022
Title Time and Gödel: Fuzzy temporal reasoning in PSPACE Type Other Author Aguilera -
2022
Title FUNCTORIAL FAST-GROWING HIERARCHIES Type Other Author Aguilera -
2024
Title Higher-Order Feedback Computation; In: Twenty Years of Theoretical and Practical Synergies - 20th Conference on Computability in Europe, CiE 2024, Amsterdam, The Netherlands, July 8-12, 2024, Proceedings DOI 10.1007/978-3-031-64309-5_24 Type Book Chapter Publisher Springer Nature Switzerland -
2024
Title Monotone versus non-monotone projective operators DOI 10.1112/blms.13194 Type Journal Article Author Aguilera J Journal Bulletin of the London Mathematical Society
Disseminations
Fundings
-
2026
Title Uncovering the Axioms of Mathematics Type Research grant (including intramural programme) DOI 10.55776/efp2661725 Start of Funding 2026 Funder Austrian Science Fund (FWF) -
2024
Title Proofs Beyond the Transfinite Type Research grant (including intramural programme) DOI 10.55776/sta139 Start of Funding 2024 Funder Austrian Science Fund (FWF)