Free Universal Algebras
Let be any set, let be an algebraic structure of type generated by . Let the underlying set of this algebraic structure, sometimes called universe, be, and let be a function. We say that, (or informally just ) is a free algebra (of type ) on the set of free generators if, for every algebra of type and function, where is a universe of, there exists a unique homomorphism such that .
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Famous quotes containing the words free and/or universal:
“I am truly free only when all human beings, men and women, are equally free. The freedom of other men, far from negating or limiting my freedom, is, on the contrary, its necessary premise and confirmation.”
—Mikhail Bakunin (1814–1876)
“I admit that the generation which produced Stalin, Auschwitz and Hiroshima will take some beating; but the radical and universal consciousness of the death of God is still ahead of us; perhaps we shall have to colonize the stars before it is finally borne in upon us that God is not out there.”
—R.J. Hollingdale (b. 1930)