In this paper, we study strong Mathias forcing and its generalizations to uncount-able cases. By applying the method of forcing, we show that strong Mathias forcing adds unbounded but not dominating reals, which is in contrast to usual Mathias forcing. We also show that theω1-version of strong Mathias forcing adds unbounded but not dominatingω1-reals and meanwhile, this forcing adds no new reals, which are applied to the consistency of cardinal invariants on the real line.%本文研究了加强型Mathias力迫及其在不可数情形下的推广.通过力迫法,证明了Mathias力迫添加支配性实数,而加强型Mathias力迫添加的是无界、非支配性的实数.还证明了ω1上的Mathias型力迫添加的是无界、非支配性的ω1类实数且不添加新的实数.这些结论可应用于对实数上的基数不变量的研究.
展开▼
