Journal of Symbolic Logic

Presburger Arithmetic with Unary Predicates is $\Pi^1_1$ Complete

Joseph Y. Halpern

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Abstract

We give a simple proof characterizing the complexity of Presburger arithmetic augmented with additional predicates. We show that Presburger arithmetic with additional predicates is $\Pi^1_1$ complete. Adding one unary predicate is enough to get $\Pi^1_1$ hardness, while adding more predicates (of any arity) does not make the complexity any worse.

Article information

Source
J. Symbolic Logic, Volume 56, Issue 2 (1991), 637-642.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183743663

Mathematical Reviews number (MathSciNet)
MR1133091

Zentralblatt MATH identifier
0738.03017

JSTOR
links.jstor.org

Citation

Halpern, Joseph Y. Presburger Arithmetic with Unary Predicates is $\Pi^1_1$ Complete. J. Symbolic Logic 56 (1991), no. 2, 637--642. https://projecteuclid.org/euclid.jsl/1183743663


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