可独立公理化的L_{omega_1,omega}理论
Independently Axiomatizable L_{omega_1,omega} Theories
摘要：
本文部分回答了Arnie Miller（http：//www.math.wisc.edu/miller/res/problem.pdf）和X. Caicedo，我们得到了L_{omega_1,omega}理论有独立公理化的充分条件。作为结果，我们得到两个推论：第一，假设Vaught猜想，每一个L_{omega_1,omega}理论在可数语言有一个独立的公理化。第二，这一次完全在ZFC中，波莱尔集族的每个交集都可以形成为独立波莱尔集族的交集。
英文摘要：
In partial answer to a question posed by Arnie Miller (http://www.math.wisc.edu/~miller/res/problem.pdf) and X. Caicedo, we obtain sufficient conditions for an L_{omega_1,omega} theory to have an independent axiomatization. As a consequence we obtain two corollaries: The first, assuming Vaught's Conjecture, every L_{omega_1,omega} theory in a countable language has an independent axiomatization. The second, this time outright in ZFC, every intersection of a family of Borel sets can be formed as the intersection of a family of independent Borel sets.
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。
