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Showing 1 to 6 of 6 for “"Constructive Mathematics"”.
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Constructive Analysis of Partial Differential Equations
… of the Dirichlet Problem within Errett Bishop's constructive mathematics. It roughly falls into three major parts: a critical analysis of the classical approaches from a constructive point of view (Chapter 2); constructive results on the existence, stability, and maximality of weak solutions …
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Proof-Theoretical Aspects of Well Quasi-Orders and Phase Transitions in Arithmetical Provability
… of proof theory - more precisely, in reverse mathematics and constructive mathematics. Reversed mathematics, proposed by Harvey Friedman, aims to classify the strength of mathematical theorems by identifying the required axioms. In this framework, we focus on two classical results relative to …
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Kontinuum und Konstitution der Wirklichkeit
… are compared with models of todays logic and mathematics. There is considerd constructive mathematics, the logic of perception from Bell, Blau's Logic of reflection and a model of Myrvold. Then there is developed a new model.
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Computability and Structure
This dissertation contains results in the area of constructive mathematics with emphasis to computable algebra and computable analysis. Mal'cev [66] and Rabin [86] initiated the study of computable groups, and Turing [96, 95] started the investigation of effective procedures in analysis. The thesis …
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Semantic and Mathematical Foundations for Intuitionism
… the proper foundation for the intuitionistic mathematics whose development began with L.E.J. Brouwer's work in the first half of the 20th Century. It is taken for granted by most philosophers, logicians, and mathematicians interested in foundational questions that intuitionistic mathematics …
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Homogeneous models and their toposes of supported sets
This thesis studies homogeneous models by looking at their topos of finitely supported sets. Of various well-known toposes, such as cubical sets and simplicial sets, it is shown that they can be presented as a topos of this kind. It is argued that these examples can be understood as coming from a …