非唯一的宇宙
The non-unique Universe
摘要：
本文的目的是借助数理逻辑中的概念和定理，阐明多元宇宙的存在在数学物理中是逻辑必然的条件，以及哥德尔不完备性定理对万物理论的意义。在最后一节中得到三个结论：（i）我们宇宙的结构理论可能是一个不可判定的理论，这构成了数学物理的一个潜在的认识论极限，但是因为这样的理论必须是完整的，所以对于存在一个最终的万物理论没有本体论障碍;（ii）在数理逻辑方面，有两种不同类型的多元宇宙：类的非同构，但elementarily等价的模型，和类的模型，这是既非同构和elementarily不等价的;（iii）对于一个假设的理论的一切只有一个可能的模型，从而否定可能存在的多元宇宙，该理论必须是这样的，它承认只有一个有限的模型。
英文摘要：
The purpose of this paper is to elucidate, by means of concepts and theorems drawn from mathematical logic, the conditions under which the existence of a multiverse is a logical necessity in mathematical physics, and the implications of Godel's incompleteness theorem for theories of everything. Three conclusions are obtained in the final section: (i) the theory of the structure of our universe might be an undecidable theory, and this constitutes a potential epistemological limit for mathematical physics, but because such a theory must be complete, there is no ontological barrier to the existence of a final theory of everything; (ii) in terms of mathematical logic, there are two different types of multiverse: classes of non-isomorphic but elementarily equivalent models, and classes of model which are both non-isomorphic and elementarily inequivalent; (iii) for a hypothetical theory of everything to have only one possible model, and to thereby negate the possible existence of a multiverse, that theory must be such that it admits only a finite model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
