Mathias 力迫与 Silver 力迫的恰当与非恰当变体
Proper and Improper Variants of Mathias and Silver Forcing
AI总结：
该研究解答了 Mathias 与 Silver 力迫密度变体的恰当性及添加支配实数、Cohen 实数等问题，并将证明推广到满足条件的下半连续子测度参数化 Mathias 力迫。
摘要：
本文回答了 arXiv:2102.06009 中关于 Mathias 力迫和 Silver 力迫的密度变体的若干问题。这些问题包括：每种力迫是否恰当、是否添加支配实数，或是否添加 Cohen 实数。我们还将其中一个证明推广到由满足某些性质的下半连续子测度参数化的 Mathias 力迫。
英文摘要：
In this paper we answer several questions in arXiv:2102.06009 regarding density variants of Mathias and Silver forcing. These questions include whether each of the forcing is proper, add dominating real, or add Cohen real. We also generalize one of the proofs to Mathias forcings parametrized by lower semi-continuous submeasures satisfying certain properties.
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。
