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:
“Whatever does not spring from a man’s free choice, or is only the result of instruction and guidance, does not enter into his very being, but still remains alien to his true nature; he does not perform it with truly human energies, but merely with mechanical exactness.”
—Karl Wilhelm Von Humboldt (1767–1835)
“We can most safely achieve truly universal tolerance when we respect that which is characteristic in the individual and in nations, clinging, though, to the conviction that the truly meritorious is unique by belonging to all of mankind.”
—Johann Wolfgang Von Goethe (1749–1832)