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Anti-Specker Properties in Constructive Reverse Mathematics

Constructive reverse mathematics is a programme in which non- and semi-constructive principles are classified in accordance with which other principles they imply or are implied by, relative to the framework of Bishop-style constructive mathematics. One such principle that has come under focus in recent years is an antithesis of Specker's theorem (that theorem being a characteristic result of Russian recursive mathematics): this so-called anti-Specker property is intuitionistically valid, and of considerable utility in proving results of real and complex analysis.

We introduce several new weakenings of the anti-Specker property and explore their role in constructive reverse mathematics, identifying implication relationships that they stand in to other notable principles. These include, but are not limited to: variations upon Brouwer's fan theorem, certain compactness properties, and so-called zero-stability properties. We also give similar classification results for principles arising directly from Specker's theorem itself, and present new, direct proofs of related fan-theoretic results.

We investigate how anti-Specker properties, alongside power-series-based arguments, enable us to recover information about the structure of holomorphic functions: in particular, they allow us to streamline a sequence of maximum-modulus theorems.

Identiferoai:union.ndltd.org:canterbury.ac.nz/oai:ir.canterbury.ac.nz:10092/9169
Date January 2013
CreatorsDent, James Edgar
PublisherUniversity of Canterbury. Department of Mathematics and Statistics
Source SetsUniversity of Canterbury
LanguageEnglish
Detected LanguageEnglish
TypeElectronic thesis or dissertation, Text
RightsCopyright James Edgar Dent, http://library.canterbury.ac.nz/thesis/etheses_copyright.shtml
RelationNZCU

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