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Fall 1995 The Theory of $\kappa$-like Models of Arithmetic
Richard Kaye
Notre Dame J. Formal Logic 36(4): 547-559 (Fall 1995). DOI: 10.1305/ndjfl/1040136915

Abstract

A model $(M,<,\ldots)$ is said to be $\kappa$-like if $\mbox{card $\;$} M =\kappa$ but for all $a\in M$, $\mbox{card}\{x \in M: x< a\}< \kappa$. In this paper, we shall study sentences true in $\kappa$-like models of arithmetic, especially in the cases when $\kappa$ is singular. In particular, we identify axiom schemes true in such models which are particularly `natural' from a combinatorial or model-theoretic point of view and investigate the properties of models of these schemes.

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Richard Kaye. "The Theory of $\kappa$-like Models of Arithmetic." Notre Dame J. Formal Logic 36 (4) 547 - 559, Fall 1995. https://doi.org/10.1305/ndjfl/1040136915

Information

Published: Fall 1995
First available in Project Euclid: 17 December 2002

zbMATH: 0848.03019
MathSciNet: MR1368466
Digital Object Identifier: 10.1305/ndjfl/1040136915

Subjects:
Primary: 03C62
Secondary: 03C55

Rights: Copyright © 1995 University of Notre Dame

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Vol.36 • No. 4 • Fall 1995
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