The article presents an algebraic theory of values (W-system) based on the ideas of Tadeusz Czezowski. According to Czezowski, 'x' is a value if there is a ternary value-generating relation that holds between 'x', a valuating subject and a value-parameter. Values enter into various relations: equality, comparability and incomparability. W-system distinguishes between values and their carriers and introduces formal definitions of some other relations between values: being lesser (greater), exclusion, concurrence and contradiction. W-system provides answers to the following questions: What is the formal structure of values? What relations hold between values and their carriers? Do values exist? An axiomatic theory of values is presented in this article. The basis of this theory is Czezowski's idea of values
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