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:
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And choosing forced on free will: fire or ice.”
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“I have been maintaining that the meaning of the word ‘ought’ and other moral words is such that a person who uses them commits himself thereby to a universal rule. This is the thesis of universalizability.”
—Richard M. Hare (b. 1919)