Name
Abstract | ||
|---|---|---|
A transitive model M of ZFC is called a ground if the universe V is a set, forcing extension of M. We show that the grounds of V are downward set-directed. (Consequently, we establish some fundamental theorems on the forcing method and the set-theoretic geology. For instance, (1) the mantle, the intersection of all grounds, must be a model of ZFC. (2) V has only set many grounds if and only if the mantle is a ground. We also show that if the universe has some very large cardinal, then the mantle must, be a ground. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1142/S021906131750009X | JOURNAL OF MATHEMATICAL LOGIC |
Keywords | Field | DocType |
Forcing method,set-theoretic geology,downward directed grounds hypothesis,large cardinal,generic multiverse | Discrete mathematics,Large cardinal,Cardinal number,Mantle (geology),Forcing (mathematics),If and only if,Universe,Mathematics,Transitive relation | Journal |
Volume | Issue | ISSN |
17 | 2 | 0219-0613 |
Citations | PageRank | References |
3 | 0.46 | 4 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Toshimichi Usuba | 1 | 14 | 4.99 |