Cohen \(\cal M8\): Apter's Model | Historical notes
Description: Suppose \(\cal M \models ZFC +\) "There arecardinals \(\kappa \le \delta \le \lambda\) such that \(\kappa\) is a supercompact limit of supercompact cardinals, \(\lambda\) is a measurable cardinal, and \(\delta\) is \(\lambda\) supercompact." (See, for example, Drake [1974], Kanamori/Magador [1978], or Solovay/Reinhardt/Kanamori [1978] for information about large cardinals.) \(\cal M8\) is constructed by first forcing over the ground model \(\cal M\), constructing an inner model \(\cal M'\), doing an additional forcing argument over \(\cal M'\), and then constructing the final inner model \(\cal M8\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M8\):
0,
All Forms Known to be False in \(\cal M8\):
430-p,
427,
426,
407,
391,
359,
347,
345,
335-n,
334,
333,
292,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
218,
202,
192,
181,
174-alpha,
168,
164,
149,
147,
133,
114,
113,
112,
109,
101,
100,
95-F,
91,
90,
89,
87-alpha,
86-alpha,
67,
66,
51,
44,
43,
40,
39,
28-p,
25,
23,
21,
20,
8,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 0
Falses that are implied by others list: 8-25-91
References for models trues falses list: References Apter [1985a], notes 18 and 20.
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