Cohen \(\cal M42\): Bull's Model | Historical notes
Description: Let \(\cal M\) be a countable transitive model of \(ZFC +\) "There are uncountable regular cardinals \(\aleph_\alpha <\aleph_\beta < \aleph_\gamma\) such that \(\aleph_\alpha\) is \(\aleph_\gamma\)-supercompact; \(\aleph_\beta\) is the first measurable cardinal greater than \(\aleph_\alpha\); and \(\aleph_\gamma =|2^{\aleph_\beta}|\)." Using backward Easton forcing (which is due to Silver), Bull constructs a generic extension of \(\cal M\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M42\):
423,
420,
419,
418,
404,
390,
389,
387,
380,
379,
378,
377,
376,
374-n,
373-n,
362,
361,
358,
357,
355,
354,
353,
352,
351,
350,
342-n,
341,
340,
338,
336-n,
325,
304,
296,
288-n,
282,
249,
217,
216,
209,
199(\(n\)),
198,
196-alpha,
194,
185,
182,
167,
150,
132,
131,
128,
127,
126,
124,
119,
108,
104,
98,
94,
86-alpha,
84,
83,
82,
80,
74,
73,
64,
57,
39,
38,
35,
34,
32,
31,
29,
27,
26,
24,
19,
18,
17,
16,
13,
12,
11,
10,
9,
8,
6,
5,
0,
All Forms Known to be False in \(\cal M42\):
430-p,
427,
391,
335-n,
334,
333,
321,
320,
319,
292,
264,
239,
218,
202,
164,
163,
149,
147,
133,
117,
114,
112,
109,
95-F,
91,
90,
89,
67,
66,
28-p,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 39-86
Falses that are implied by others list: 91-163-321
References for models trues falses list: ReferencesBull [1978], Brunner [1982a], notes 18 and 20.
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