Journal of Symbolic Logic

Structure with fast elimination of quantifiers

Mihai Prunescu

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 22 February 2006

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B05: Classical propositional logic 03B25: Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]


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

Export citation


  • Christine Gaßner A structure of finite signature with identity relation and with $\textupP=\textupNP$---A formal proof, preprint, Universität Greifswald, 2004.
  • Armin Hemmerling $\textupP=\textupNP$ for some structures over the binary words, Journal of Complexity, vol. 21 (2005), no. 4, pp. 557--578.
  • Saul Kripke Outline of a theory of truth, The Journal of Philosophy, vol. 72 (1975), no. 19, pp. 690--716.
  • Bruno Poizat Les petits cailloux, ALEAS, Lyon,1995.
  • -------- Une tentative malheureuse de construire une structure eliminant rapidement les quanteurs, Lecture Notes in Computer Science, vol. 1862,2000, pp. 61--70.
  • Mihai Prunescu Non-effective quantifier elimination, Mathematical Logic Quarterly, vol. 47 (2001), no. 4, pp. 557--561.