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In model theory, a branch of mathematical logic, a C-minimal theory is a theory that is "minimal" with respect to a ternary relation ''C'' with certain properties. Algebraically closed fields with a (Krull) valuation are perhaps the most important example. This notion was defined in analogy to the o-minimal theories, which are "minimal" (in the same sense) with respect to a linear order. ==Definition== A ''C''-relation is a ternary relation ''C''(''x'';''yz'') that satisfies the following axioms. # # # # A C-minimal structure is a structure ''M'', in a signature containing the symbol ''C'', such that ''C'' satisfies the above axioms and every set of elements of ''M'' that is definable with parameters in ''M'' is a Boolean combination of instances of ''C'', i.e. of formulas of the form ''C''(''x'';''bc''), where ''b'' and ''c'' are elements of ''M''. A theory is called C-minimal if all of its models are C-minimal. A structure is called strongly C-minimal if its theory is C-minimal. One can construct C-minimal structures which are not strongly C-minimal. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「C-minimal theory」の詳細全文を読む スポンサード リンク
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