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Proof Theory
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The article was published on 1975-01-01 and is currently open access. It has received 770 citations till now. The article focuses on the topics: Proof theory & Gentzen's consistency proof.read more
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The Godel Hierarchy and Reverse Mathematics
TL;DR: In 1900, the great mathematician David Hilbert laid down a list of 23 mathematical problems which exercised a great influence on subsequent mathematical research as mentioned in this paper, and it is noteworthy that Hilbert's Problems 1 and 2 are squarely in the area of foundations of mathematics, while Problems 10 and 17 turned out to be closely related to mathematical logic.
Journal ArticleDOI
On the number of steps in proofs
TL;DR: This paper proves some results about the complexity of proofs in Hilbert-style formal systems such as in [17], and shows a bound on the number of steps in a cut-free proof, some speed-up results, and bounds on theNumber of Steps in proofs of Paris-Harrington sentences.
Journal Article
Explicit Environments
TL;DR: In this paper, a simply typed λβ-calculus with environments as first class values is introduced, which has desirable properties such as subject reduction, confluence, conservativity, and strong normalizability.
Journal ArticleDOI
A generalization of the Second Incompleteness Theorem and some exceptions to it
TL;DR: The notion of a naming convention is introduced and this paradigm is used to both develop a new version of the Second Incompleteness Theorem and to describe when an axiom system can partially evade the Second incompleville Theorem.
Journal ArticleDOI
The event bush as a semantic-based numerical approach to natural hazard assessment (exemplified by volcanology)
Cyril Pshenichny,Sergey I. Nikolenko,Roberto Carniel,P. A. Vaganov,Z. V. Khrabrykh,V. P. Moukhachov,V. L. Akimova-Shterkhun,A. A. Rezyapkin +7 more
TL;DR: The event bush is a new formalism for organizing knowledge in various fields of geoscience, particularly suitable for hazard assessment purposes, and the connection with Bayesian belief networks is presented.