Remarks on formalized arithmetic and subsystems thereof

Title: Remarks on formalized arithmetic and subsystems thereof
Creator: Brink, C
ThesisAdvisor: Schutte, H J
Subject: Gödel, Kurt
Subject: Logic, Symbolic and mathematical
Subject: Semantics (Philosophy)
Subject: Arithmetic -- Foundations
Subject: Number theory
Date: 1975
Type: Thesis
Type: Masters
Type: MSc
Identifier: vital:5424
Identifier: http://hdl.handle.net/10962/d1009752
Identifier: Gödel, Kurt
Identifier: Logic, Symbolic and mathematical
Identifier: Semantics (Philosophy)
Identifier: Arithmetic -- Foundations
Identifier: Number theory
Description: In a famous paper of 1931, Gödel proved that any formalization of elementary Arithmetic is incomplete, in the sense that it contains statements which are neither provable nor disprovable. Some two years before this, Presburger proved that a mutilated system of Arithmetic, employing only addition but not multiplication, is complete. This essay is partly an exposition of a system such as Presburger's, and partly an attempt to gain insight into the source of the incompleteness of Arithmetic, by linking Presburger's result with Gödel's.
Format: 119 pages, pdf
Publisher: Rhodes University, Faculty of Science, Mathematics
Language: English
Rights: Brink, C

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