On Sets of Relations Definable by Addition

Lynch, James F.

J. Symbolic Logic, Tome 47 (1982) no. 1, p. 659-668 / Harvested from Project Euclid

Résumé

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.

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Publié le : 1982-09-14
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