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A definable set which is the complement of an analytic set.

A ring is commutative if the multiplication operation is commutative.

All lengths can be expressed as real numbers.

A type I Markov move.

An analytic, Borel, or coanalytic set.

For a finite group of h elements with an n_ith dimensional ith irreducible representation, sum_(i)n_i^2=h.

A simple graph with n>=3 graph vertices in which each graph vertex has vertex degree >=n/2 has a Hamiltonian cycle.

An equilibrium point in game theory is a set of strategies {x^^_1,...,x^^_n} such that the ith payoff function K_i(x) is larger or equal for any other ith strategy, i.e., ...

If a Sylow 2-subgroup T of G lies in a unique maximal 2-local P of G, then P is a "strongly embedded" subgroup of G, and G is known.

A graded algebra over the integers Z. Cohomology of a space is a graded ring.