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Hyperuniformity and non-hyperuniformity of zeros of Gaussian Weyl-Heisenberg Functions. [PDF]
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Applied Proof Theory: Proof Interpretations and Their Use in Mathematics
Springer Monographs in Mathematics, 2008U. Kohlenbach
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The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas.
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A theory of classes: proofs and models
Mathematical Structures in Computer Science, 1997We investigate the proof structure and models of theories of classes, where classes are ‘collections’ of entities. The theories are weaker than set theories and arise from a study of type classes in programming languages, as well as from comprehension schemata in categories. We introduce two languages of proofs: one a simple type theory and the
Hilken, Barney P, Rydeheard, David E
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Theories and Ordinals in Proof Theory
Synthese, 2006The author gives a very good survey on the aims and techniques of ordinal analysis. It includes not only the classical topics of subsystems of second-order arithmetic and of set theory, but also newer developments in relation to model-theoretic characterizations (partial models and patterns of resemblance; Sec.~4), characterizations via \(E\)-recursion
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2000
This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category ...
Troelstra, A.S., Schwichtenberg, H.
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This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category ...
Troelstra, A.S., Schwichtenberg, H.
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Proof Theory of Constructive Systems: Inductive Types and Univalence
, 2016In Feferman’s work, explicit mathematics and theories of generalized inductive definitions play a central role. One objective of this article is to describe the connections with Martin–Lof type theory and constructive Zermelo–Fraenkel set theory.
M. Rathjen
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