Determinacy in Second-Order Arithmetic

Determinacy in Second-Order Arithmetic

Juan P. Aguilera (ORCID: 0000-0002-2768-6714)

Disciplines

Mathematics (100%)

Keywords

    Second-Order Arithmetic, Reverse Mathematics, Monotone Induction, Beta-Model, Kripke-Platek Set Theory

Abstract

Reverse Mathematics is the branch of logic which studies which axioms are necessary in order to prove specific mathematical theorems. It mostly deals with subsystems of second-order arithmetic. Determinacy principles assert that various infinite games are determined. These can be regarded both as axioms and as mathematical theorems. The goal of the project is to study the precise relation between determinacy principles and subsystems of second- order arithmetic.
Research institution(s)
International project participants

Research Output

  • 1 Citations
  • 5 Publications
  • 1 Scientific Awards
Publications
  • 2023
    Title EFFECTIVE CARDINALS AND -DETERMINACY
    DOI 10.1017/jsl.2023.90
    Type Journal Article
    Author Aguilera J
    Journal The Journal of Symbolic Logic
    Pages 1-8
  • 2024
    Title The Limits of Determinacy in Higher-Order Arithmetic
    DOI 10.48550/arxiv.2411.04786
    Type Preprint
    Author Aguilera J
  • 2024
    Title Functorial Fast-Growing Hierarchies
    DOI 10.1017/fms.2023.128
    Type Journal Article
    Author Aguilera J
    Journal Forum of Mathematics, Sigma
    Link Publication
  • 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
    Pages 256-264
    Link Publication
  • 2025
    Title The metamathematics of separated determinacy
    DOI 10.1007/s00222-025-01322-3
    Type Journal Article
    Author Aguilera J
    Journal Inventiones mathematicae
    Pages 313-457
    Link Publication
Scientific Awards
  • 2025
    Title CNRL Award 2025
    Type Research prize
    Level of Recognition National (any country)