Journal of Symbolic Logic

On Sets of Relations Definable by Addition

James F. Lynch

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Abstract

For every $k \in \omega$, there is an infinite set $A_k \subseteq \omega$ and a $d(k) \in \omega$ such that for all $Q_0, Q_1 \subseteq A_k$ where $|Q_0| = |Q_1$ or $d(k) < |Q_0|, |Q_1| < \aleph_0$, the structures $\langle \omega, +, Q_0\rangle$ and $\langle \omega, +, Q_1\rangle$ are indistinguishable by first-order sentences of quantifier depth $k$ whose atomic formulas are of the form $u = v, u + v = w$, and $Q(u)$, where $u, v$, and $w$ are variables.

Article information

Source
J. Symbolic Logic, Volume 47, Issue 3 (1982), 659-668.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183741093

Mathematical Reviews number (MathSciNet)
MR666823

Zentralblatt MATH identifier
0504.03013

JSTOR
links.jstor.org

Citation

Lynch, James F. On Sets of Relations Definable by Addition. J. Symbolic Logic 47 (1982), no. 3, 659--668. https://projecteuclid.org/euclid.jsl/1183741093


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