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:
“The American adolescent, then, is faced, as are the adolescents of all countries who have entered or are entering the machine age, with the question: freedom from what and at what price? The American feels so rich in his opportunities for free expression that he often no longer knows what it is he is free from. Neither does he know where he is not free; he does not recognize his native autocrats when he sees them.”
—Erik H. Erikson (1904–1994)
“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)