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2012 The Usual Model Construction for NFU Preserves Information
M. Randall Holmes
Notre Dame J. Formal Logic 53(4): 571-580 (2012). DOI: 10.1215/00294527-1722764

Abstract

The usual construction of models of NFU (New Foundations with urelements, introduced by Jensen) is due to Maurice Boffa. A Boffa model is obtained from a model of (a fragment of) Zermelo–Fraenkel with Choice (ZFC) with an automorphism which moves a rank: the domain of the Boffa model is a rank that is moved. “Most” elements of the domain of the Boffa model are urelements in terms of the interpreted NFU. The main result of this paper is that the restriction of the membership relation of the original model of set theory with automorphism to the domain of the Boffa model is first-order definable in the language of NFU. In particular, all information about the extensions in the original model of the urelements of the model of NFU is definable in terms of NFU. A corollary (answering a question of Thomas Forster) is that the urelements in a Boffa model are not homogeneous.

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M. Randall Holmes. "The Usual Model Construction for NFU Preserves Information." Notre Dame J. Formal Logic 53 (4) 571 - 580, 2012. https://doi.org/10.1215/00294527-1722764

Information

Published: 2012
First available in Project Euclid: 8 November 2012

zbMATH: 1284.03239
MathSciNet: MR2995421
Digital Object Identifier: 10.1215/00294527-1722764

Subjects:
Primary: 03E70

Rights: Copyright © 2012 University of Notre Dame

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