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  1. Reverse mathematics and Peano categoricity.Stephen G. Simpson & Keita Yokoyama - 2013 - Annals of Pure and Applied Logic 164 (3):284-293.
    We investigate the reverse-mathematical status of several theorems to the effect that the natural number system is second-order categorical. One of our results is as follows. Define a system to be a triple A,i,f such that A is a set and i∈A and f:A→A. A subset X⊆A is said to be inductive if i∈X and ∀a ∈X). The system A,i,f is said to be inductive if the only inductive subset of A is A itself. Define a Peano system to be (...)
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  • Second order logic or set theory?Jouko Väänänen - 2012 - Bulletin of Symbolic Logic 18 (1):91-121.
    We try to answer the question which is the “right” foundation of mathematics, second order logic or set theory. Since the former is usually thought of as a formal language and the latter as a first order theory, we have to rephrase the question. We formulate what we call the second order view and a competing set theory view, and then discuss the merits of both views. On the surface these two views seem to be in manifest conflict with each (...)
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  • Über Grenzzahlen und Mengenbereiche: Neue Untersuchungen über die Grundlagen der Mengenlehre.Ernst Zermelo - 1930 - Fundamenta Mathematicæ 16:29--47.
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  • Completeness in the theory of types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.
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  • Axioms of Infinity as the Starting Point for Rigorous Mathematics.John P. Burgess - 2012 - Annals of the Japan Association for Philosophy of Science 20:17-28.
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