The Operational Perspective: Three Routes

DOI10.1007/978-3-319-29198-7_7zbMath1439.03018OpenAlexW2485820297MaRDI QIDQ3305557

Solomon Feferman

Publication date: 7 August 2020

Published in: Advances in Proof Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-29198-7_7

zbMATH Keywords

proof theorytruth predicatesubstitution ruletransfinite inductioninduction axiom

Mathematics Subject Classification ID

Philosophical and critical aspects of logic and foundations (03A05) Metamathematics of constructive systems (03F50) Proof theory in general (including proof-theoretic semantics) (03F03)

Related Items

IN MEMORIAM: SOLOMON FEFERMAN (1928–2016), Unfolding Schematic Systems, The Operational Penumbra: Some Ontological Aspects, Reflecting and unfolding, A new model construction by making a detour via intuitionistic theories. II: Interpretability lower bound of Feferman's explicit mathematics \(T_0\)

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
• 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
• Operational closure and stability
• Relativized ordinal analysis: the case of power Kripke-Platek set theory
• 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
• Full operational set theory with unbounded existential quantification and power set
• Monotone inductive definitions in a constructive theory of functions and classes
• The \(\mu\) quantification operator in explicit mathematics with universes and iterated fixed point theories with ordinals
• Systems of explicit mathematics with non-constructive \(\mu\)-operator. I
• On the proof-theoretic strength of monotone induction in explicit mathematics
• The unfolding of non-finitist arithmetic
• Towards a computation system based on set theory
• A set of postulates for the foundation of logic. II
• Totality in applicative theories
• Systems of explicit mathematics with non-constructive \(\mu\)-operator. II
• On Feferman's operational set theory \textsf{OST}
• Systems of explicit mathematics with non-constructive \(\mu\)-operator and join
• Extending constructive operational set theory by impredicative principles
• Choice principles, the bar rule and autonomously iterated comprehension schemes in analysis
• UNFOLDING FINITIST ARITHMETIC
• The strength of admissibility without foundation
• Reflecting on incompleteness
• Normal functions and constructive ordinal notations
• Outline of a Theory of Truth
• A well-ordering proof for Feferman's theoryT 0
• Monotone inductive definitions in explicit mathematics
• Power Kripke–Platek set theory and the axiom of choice
• Theories of Proof-Theoretic Strength Ψ (Γ_Ω +1)
• The system CΔ of combinatory logic
• Systems of predicative analysis
• RELATIVIZING OPERATIONAL SET THEORY
• Eine Grenze Für die Beweisbarkeit der Transfiniten Induktion in der Verzweigten Typenlogik
• Describing ordinals using functionals of transfinite type
• On the relationship between ATR₀ and
• What is Cantor's Continuum Problem?
• The strength of Mac Lane set theory