A new model construction by making a detour via intuitionistic theories. II: Interpretability lower bound of Feferman's explicit mathematics \(T_0\)
From MaRDI portal
Publication:2344720
DOI10.1016/j.apal.2015.04.002zbMath1371.03093OpenAlexW648945431MaRDI QIDQ2344720
Publication date: 15 May 2015
Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apal.2015.04.002
interpretabilityextensional realizabilityFeferman's explicit mathematicsmaking a detour via intuitionistic theoriestree representation of sets
Axiomatics of classical set theory and its fragments (03E30) Second- and higher-order arithmetic and fragments (03F35) Metamathematics of constructive systems (03F50) Intuitionistic mathematics (03F55) Combinatory logic and lambda calculus (03B40) Relative consistency and interpretations (03F25)
Related Items
A MARRIAGE OF BROUWER’S INTUITIONISM AND HILBERT’S FINITISM I: ARITHMETIC, Characterizations of ordinal analysis, Research on supply chain risk assessment with intuitionistic fuzzy information, Elementary inductive dichotomy: separation of open and clopen determinacies with infinite alternatives, The Operational Penumbra: Some Ontological Aspects, Proof Theory of Constructive Systems: Inductive Types and Univalence, A new model construction by making a detour via intuitionistic theories. III: Ultrafinitistic proofs of conservations of \(\Sigma_1^1\) collection
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience
- A new model construction by making a detour via intuitionistic theories. I: Operational set theory without choice is \(\Pi_1\)-equivalent to KP
- The Suslin operator in applicative theories: its proof-theoretic analysis via ordinal theories
- Operational set theory and small large cardinals
- Monotone inductive definitions in a constructive theory of functions and classes
- Systems of explicit mathematics with non-constructive \(\mu\)-operator. I
- The strength of some Martin-Löf type theories
- On the proof-theoretic strength of monotone induction in explicit mathematics
- Extensional realizability
- Realization of constructive set theory into explicit mathematics: A lower bound for impredicative Mahlo universe
- Reflections on reflections in explicit mathematics
- Interpreting classical theories in constructive ones
- Upper bounds for metapredicative Mahlo in explicit mathematics and admissible set theory
- Kripke-Platek Set Theory and the Anti-Foundation Axiom
- EXPLICIT MATHEMATICS AND OPERATIONAL SET THEORY: SOME ONTOLOGICAL COMPARISONS
- The Operational Perspective: Three Routes
- Explicit mathematics with the monotone fixed point principle
- Explicit mathematics with the monotone fixed point principle. II: Models
- Wellordering proofs for metapredicative Mahlo
- A well-ordering proof for Feferman's theoryT 0
- Monotone inductive definitions in explicit mathematics
- On the intuitionistic strength of monotone inductive definitions
- Universes in explicit mathematics
- Extending the system T\(_0\) of explicit mathematics: The limit and Mahlo axioms