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- Title
First-Order Reasoning and Primitive Recursive Natural Number Notations.
- Authors
Isles, David
- Abstract
If the collection of models for the axioms $${\mathfrak{A}}$$ of elementary number theory (Peano arithmetic) is enlarged to include not just the “natural numbers” or their non-standard infinitistic extensions but also what are here called “primitive recursive notations”, questions arise about the reliability of first-order derivations from $${\mathfrak{A}}$$. In this enlarged set of “models” some derivations usually accepted as “reliable” may be problematic. This paper criticizes two of these derivations which claim, respectively, to establish the totality of exponentiation and to prove Euclid’s theorem about the infinity of primes.
- Subjects
AXIOMS; NUMBER theory; ARITHMETIC; NATURAL numbers; EUCLIDEAN algorithm; GREATEST integer function; FOUNDATIONS of mathematical analysis
- Publication
Studia Logica, 2010, Vol 96, Issue 1, p49
- ISSN
0039-3215
- Publication type
Article
- DOI
10.1007/s11225-010-9272-4