## Journal of Symbolic Logic

### Structure with fast elimination of quantifiers

Mihai Prunescu

#### Abstract

A structure of finite signature is constructed so that: for all existential formulas ∃y⃗ φ(x⃗,y⃗) and for all tuples of elements ⃗ of the same length as the tuple x⃗, one can decide in a quadratic time depending only on the length of the formula, if ∃y⃗ φ(u⃗,y⃗) holds in the structure. In other words, the structure satisfies the relativized model-theoretic version of P=NP in the sense of [4]. This is a model-theoretical approach to results of Hemmerling and Gaßner.

#### Article information

Source
J. Symbolic Logic, Volume 71, Issue 1 (2006), 321-328.

Dates
First available in Project Euclid: 22 February 2006

https://projecteuclid.org/euclid.jsl/1140641177

Digital Object Identifier
doi:10.2178/jsl/1140641177

Mathematical Reviews number (MathSciNet)
MR2210070

Zentralblatt MATH identifier
1100.03018

#### Citation

Prunescu, Mihai. Structure with fast elimination of quantifiers. J. Symbolic Logic 71 (2006), no. 1, 321--328. doi:10.2178/jsl/1140641177. https://projecteuclid.org/euclid.jsl/1140641177

#### References

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• Mihai Prunescu Non-effective quantifier elimination, Mathematical Logic Quarterly, vol. 47 (2001), no. 4, pp. 557--561.