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Quantifier elimination is the removal of all quantifiers (the universal quantifier forall and existential quantifier exists ) from a quantified system. A first-order theory ...

An infinite sequence of positive integers a_i satisfying 1<=a_1<a_2<a_3<... (1) is an A-sequence if no a_k is the sum of two or more distinct earlier terms (Guy 1994). Such ...

This theorem states that, for a partial differential equation involving a time derivative of order n, the solution is uniquely determined if time derivatives up to order n-1 ...

A module M over a unit ring R is called faithful if for all distinct elements a, b of R, there exists x in M such that ax!=bx. In other words, the multiplications by a and by ...

Let x=(x_1,x_2,...,x_n) and y=(y_1,y_2,...,y_n) be nonincreasing sequences of real numbers. Then x majorizes y if, for each k=1, 2, ..., n, sum_(i=1)^kx_i>=sum_(i=1)^ky_i, ...

A formula of first-order logic is in prenex normal form if it is of the form Q_1x_1...Q_nx_nM, (1) where each Q_i is a quantifier forall ("for all") or exists ("exists") and ...

In the usual diagram of inclusion homomorphisms, if the upper two maps are injective, then so are the other two. More formally, consider a space X which is expressible as the ...

Serre's problem, also called Serre's conjecture, asserts that the implication "free module ==> projective module" can be reversed for every module over the polynomial ring ...

The Grötzsch graph is smallest triangle-free graph with chromatic number four. It is identical to the Mycielski graph of order four, and is implemented as ...

Isolated resonances in a dynamical system can cause considerable distortion of preserved tori in their neighborhood, but they do not introduce any chaos into a system. ...