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Consider a clause (disjunction of literals) obtained from those of a first-order logic formula Phi in Skolemized form forall x_1... forall x_nS. Then an atomic statement ...

The likelihood of a simple graph is defined by starting with the set S_1={(K_11)}. The following procedure is then iterated to produce a set of graphs G_n of order n. At step ...

An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually ...

If n=1,2 (mod 4), and the squarefree part of n is divisible by a prime p=3 (mod 4), then no difference set of order n exists. Equivalently, if a projective plane of order n ...

The symbol +/- is used to denote a quantity which should be both added and subtracted, as in a+/-b. The symbol can be used to denote a range of uncertainty, or to denote a ...

A transversal design TD_lambda(k,n) of order n, block size k, and index lambda is a triple (V, G, B) such that 1. V is a set of kn elements, 2. G is a partition of V into k ...

A series is an infinite ordered set of terms combined together by the addition operator. The term "infinite series" is sometimes used to emphasize the fact that series ...

The set of terms of first-order logic (also known as first-order predicate calculus) is defined by the following rules: 1. A variable is a term. 2. If f is an n-place ...

Tarski's theorem says that the first-order theory of reals with +, *, =, and > allows quantifier elimination. Algorithmic quantifier elimination implies decidability assuming ...

A schematic diagram used in logic theory to depict collections of sets and represent their relationships. The Venn diagrams on two and three sets are illustrated above. The ...