论文标题
关于数学的一致性和存在
On consistency and existence in mathematics
论文作者
论文摘要
本文提出了一个问题：“一组公理的一致性是否需要满足其满足的模型？”在弗莱格 - 希尔伯特争议的框架内。这个问题在历史上与戈德尔完整定理的表述，证明和接受有关。然后，使用数学逻辑的工具来争辩说，弗雷格是正确的，可以保持正确的感觉，以维持证明一致性尽可能困难，但希尔伯特（Hilbert）是正确的，以维持证明存在给定一致性的存在很容易。
This paper engages the question "Does the consistency of a set of axioms entail the existence of a model in which they are satisfied?" within the frame of the Frege-Hilbert controversy. The question is related historically to the formulation, proof, and reception of Gödel's Completeness Theorem. Tools from mathematical logic are then used to argue that there are precise senses in which Frege was correct to maintain that demonstrating consistency is as difficult as it can be but also in which Hilbert was correct to maintain that demonstrating existence given consistency is as easy as it can be.
