Reflection Principles and their Use for Establishing the Complexity of Axiomatic Systems

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Mathematical Logic Quarterly 14 (7-12):97-142 (1968)
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10.1002/malq.19680140702

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original Kreisel, Georg; Lévy, Azriel (1968) "Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems". Zeitschrift für Mathematische Logic Und Grundlagen der Mathematik 14(1):97--142
edition Kreisel, G. (1971) "Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems". Journal of Symbolic Logic 36(3):529-532

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Reflection Principles and Their Use for Establishing the Complexity of Axiomatic Systems.Georg Kreisel & Azriel Lévy - 1968 - Zeitschrift für Mathematische Logic Und Grundlagen der Mathematik 14 (1):97--142.
Kreisel G. and Lévy A.. Reflection principles and their use for establishing the complexity of axiomatic systems. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 14 , pp. 97–142. [REVIEW]C. F. Kent - 1971 - Journal of Symbolic Logic 36 (3):529-532.
Review: Azriel Levy, On a Spectrum of Set Theories; A. Levy, R. Vaught, Principles of Partial Reflection in the Set Theories of Zermelo and Ackermann; Azriel Levy, Ernest Nagel, Patrick Suppes, Alfred Tarski, On the Principles of Reflection in Axiomatic Set Theory. [REVIEW]J. R. Shoenfield - 1970 - Journal of Symbolic Logic 35 (3):473.
Lévy A.. Principles of reflection in axiomatic set theory. Fundamenta mathematicae, vol. 49 no. 1 , pp. 1–10.J. R. Shoenfield - 1965 - Journal of Symbolic Logic 30 (2):251-251.
Analyzing completeness of axiomatic functional systems for temporal × modal logics.Alfredo Burrieza Muñiz, Inmaculada Pérez de Guzmán Molina & Emilio J. Muñoz Velasco - 2010 - Mathematical Logic Quarterly 56 (1):89-102.
Kreisel G.. On the concepts of completeness and interpretation of formal systems. Fundamenta mathematicae, vol. 39 , pp. 103–127.Kreisel G.. Applications of mathematical logic to various branches of mathematics. Applications scientifiques de la logique mathématique, Actes du 2e Colloque International de Logique Mathématique, Paris — 25–30 août 1952, Institut Henri Poincaré, Collection de logique mathématique, ser. A no. 5, lithographed , Gauthier-Villars, Paris 1954, and E. Nauwelaerts, Louvain 1954, pp. 37–49.Robinson A. and Kreisel G.. Discussion. Applications scientifiques de la logique mathématique, Actes du 2e Colloque International de Logique Mathématique, Paris — 25–30 août 1952, Institut Henri Poincaré, Collection de logique mathématique, ser. A no. 5, lithographed , Gauthier-Villars, Paris 1954, and E. Nauwelaerts, Louvain 1954, p. 50.Kreisel G.. Models, translations, and interpretations. Mathematical interpretation of formal systems, Studies in logic and the foundations of ma. [REVIEW]William Craig - 1959 - Journal of Symbolic Logic 24 (3):236-238.
Reflection Principles in Fragments of Peano Arithmetic.Hiroakira Ono - 1987 - Mathematical Logic Quarterly 33 (4):317-333.
Elements de logique mathematique - theorie des modeles: par G. Kreisel et J.L. Krivine.Georg Kreisel & J. L. Krivine - 1967 - Dunod.
G. Kreisel. Mathematical significance of consistency proofs. The journal of symbolic logic, vol. 23 no. 2 , pp. 155–182. [REVIEW]Abraham Robinson - 1966 - Journal of Symbolic Logic 31 (1):129-129.

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Citations of this work

A survey of proof theory.G. Kreisel - 1968 - Journal of Symbolic Logic 33 (3):321-388.
Arithmetical Reflection and the Provability of Soundness.Walter Dean - 2015 - Philosophia Mathematica 23 (1):31-64.
On Reflection.Leon Horsten - 2021 - Philosophical Quarterly 71 (4):738--57.

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References found in this work

Solution of a problem of Leon Henkin.M. H. Löb - 1955 - Journal of Symbolic Logic 20 (2):115-118.
Transfinite recursive progressions of axiomatic theories.Solomon Feferman - 1962 - Journal of Symbolic Logic 27 (3):259-316.
On axiomatizability within a system.William Craig - 1953 - Journal of Symbolic Logic 18 (1):30-32.

View all 14 references / Add more references