公理系统

Fast Track to Forcing Pub Date : 2020-09-30 DOI:10.1017/9781108303866.002

Alan, Christensen Beth, Elena Dave, Beth Alan, Chris, Fred Dave, Chris Alan, Beth, Fred Elena, Dave Alan, Elena, Fred, Elena Alan, Dave, Fred Beth

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摘要

注意，在第二个示例中，公理定义了一个新术语(“identity”)。这不是一个未定义项，因为公理包含了一个定义。同样，这些公理涉及到你们在离散数学中学到的基本集合理论。为了我们的目的，我们假设所有这些基本的集合理论术语都是已知的。可以将集合论本身看作另一个公理系统，但这超出了本课程的范围。

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Axiomatic Systems

Notice that in the second example, the axioms defined a new term (“identity”). This isn’t an undefined term because the axiom includes a definition. Also, these axioms refer to basic set theory that you learned in Discrete Math. For our purposes, we will assume all of those basic set theory terms are known. It is possible to view set theory itself as another axiomatic system, but that is beyond the scope of this course.

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Fast Track to Forcing

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