Quantifier elimination (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Quantifier elimination" in English language version.

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ams.org (Global: 451^st place; English: 277^th place)

Mind: basic Presburger arithmetic — $\langle \mathbb {N} ,+,0,1\rangle$ — does not admit quantifier elimination. Nipkow (2010): "Presburger arithmetic needs a divisibility (or congruence) predicate '|' to allow quantifier elimination". Nipkow, Tobias (2010). "Linear Quantifier Elimination" (PDF). Journal of Automated Reasoning. 45 (2): 189–212. doi:10.1007/s10817-010-9183-0. S2CID 14279141. Retrieved 2022-11-12.
Szmielew 1955, Page 229 describes "the method of eliminating quantification".. Szmielew, Wanda (1955). "Elementary properties of Abelian groups". Fundamenta Mathematicae. 41 (2): 203–271. doi:10.4064/fm-41-2-203-271. MR 0072131.
Hodges 1993. Hodges, Wilfrid (1993). Model Theory. Encyclopedia of Mathematics and its Applications. Vol. 42. Cambridge University Press. doi:10.1017/CBO9780511551574. ISBN 9780521304429.

Mind: basic Presburger arithmetic — $\langle \mathbb {N} ,+,0,1\rangle$ — does not admit quantifier elimination. Nipkow (2010): "Presburger arithmetic needs a divisibility (or congruence) predicate '|' to allow quantifier elimination". Nipkow, Tobias (2010). "Linear Quantifier Elimination" (PDF). Journal of Automated Reasoning. 45 (2): 189–212. doi:10.1007/s10817-010-9183-0. S2CID 14279141. Retrieved 2022-11-12.

Mind: basic Presburger arithmetic — $\langle \mathbb {N} ,+,0,1\rangle$ — does not admit quantifier elimination. Nipkow (2010): "Presburger arithmetic needs a divisibility (or congruence) predicate '|' to allow quantifier elimination". Nipkow, Tobias (2010). "Linear Quantifier Elimination" (PDF). Journal of Automated Reasoning. 45 (2): 189–212. doi:10.1007/s10817-010-9183-0. S2CID 14279141. Retrieved 2022-11-12.

Fried & Jarden 2008, p. 171. Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11 (3rd revised ed.). Springer-Verlag. ISBN 978-3-540-77269-9. Zbl 1145.12001.