If the collection of models for the axioms 21 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 21. 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.
Studia Logica publishes original papers on various logical systems, which utilize methods of contemporary formal logic (those of algebra, model theory, proof theory, etc.). More specifically, Studia Logica invites articles on topics in general logic (as defined in 1991 Mathematical Subject Classification) and on applications of logic to other branches of knowledge such as philosophy, the methodology of science or linguistics. The distinctive feature of Studia Logica is its series of monothematic issues edited by outstanding scholars and devoted to important topics of contemporary logic or covering significant conferences. This journal is also intended as an East-West link.
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Studia Logica: An International Journal for Symbolic Logic
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