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2015 Internal Categoricity in Arithmetic and Set Theory
Jouko Väänänen, Tong Wang
Notre Dame J. Formal Logic 56(1): 121-134 (2015). DOI: 10.1215/00294527-2835038

Abstract

We show that the categoricity of second-order Peano axioms can be proved from the comprehension axioms. We also show that the categoricity of second-order Zermelo–Fraenkel axioms, given the order type of the ordinals, can be proved from the comprehension axioms. Thus these well-known categoricity results do not need the so-called “full” second-order logic, the Henkin second-order logic is enough. We also address the question of “consistency” of these axiom systems in the second-order sense, that is, the question of existence of models for these systems. In both cases we give a consistency proof, but naturally we have to assume more than the mere comprehension axioms.

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Jouko Väänänen. Tong Wang. "Internal Categoricity in Arithmetic and Set Theory." Notre Dame J. Formal Logic 56 (1) 121 - 134, 2015. https://doi.org/10.1215/00294527-2835038

Information

Published: 2015
First available in Project Euclid: 24 March 2015

zbMATH: 1372.03088
MathSciNet: MR3326591
Digital Object Identifier: 10.1215/00294527-2835038

Subjects:
Primary: 03C85
Secondary: 03B15, 03B30

Rights: Copyright © 2015 University of Notre Dame

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Vol.56 • No. 1 • 2015
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