An outlook on infinity. V: An axiomatic set theory APAS for holding the actual infinity and the potential infinity concurrently. (Chinese. English summary) Zbl 1097.01505
Summary: In a view of mathematics and epistemology, in the series of papers from I to V, the historical background and current situation of the problem of infinity are reviewed. The restriction of the repellency of two existing views on the infinity is pointed out, an outlook on the infinity to unify the actual infinity and the potential infinity into one framework are presented, and an axiomatic system of sets is established based on such a framework.
For the other parts see Zbl 1099.03506, Zbl 1097.01506, Zbl 1097.01507 and Zbl 1097.01508.
For the other parts see Zbl 1099.03506, Zbl 1097.01506, Zbl 1097.01507 and Zbl 1097.01508.
MSC:
03A05 | Philosophical and critical aspects of logic and foundations |
00A30 | Philosophy of mathematics |
01A60 | History of mathematics in the 20th century |
03-03 | History of mathematical logic and foundations |
03E70 | Nonclassical and second-order set theories |