Cohen \(\cal M32\): Sageev's Model II | Historical notes
Description: Starting with a model \(\cal M\) of \(ZF + V =L\), Sageev constructs a sequence of models \(\cal M\subseteq N_0 \subseteq N_1\subseteq\cdots\subseteq N_{\kappa}\) where \(\kappa\) is an inaccessible cardinal, \(N_0\) is Cohen's model \(\cal M1\), and \(N_{\kappa}\) is \(\cal M32\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M32\):
423,
401,
390,
389,
387,
378,
377,
374-n,
373-n,
358,
342-n,
336-n,
327,
308-p,
293,
288-n,
285,
283,
280,
276,
269,
268,
250,
249,
216,
198,
178-n-N,
146,
142,
140,
132,
127,
122,
121,
120-K,
111,
102,
93,
88,
83,
80,
73,
64,
62,
61,
57,
48-K,
47-n,
46-K,
45-n,
33-n,
30,
18,
12,
11,
10,
0,
All Forms Known to be False in \(\cal M32\):
430-p,
427,
426,
407,
391,
388,
359,
347,
346,
345,
335-n,
334,
333,
328,
292,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
218,
214,
202,
193,
192,
188,
181,
174-alpha,
168,
164,
161,
152,
149,
147,
133,
129,
126,
114,
113,
112,
109,
106,
101,
100,
95-F,
91,
90,
89,
87-alpha,
86-alpha,
71-alpha,
67,
66,
44,
43,
41,
40,
39,
28-p,
20,
9,
8,
7,
4,
3,
2,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 30-57
Falses that are implied by others list: 9-91-126
References for models trues falses list: References Sageev [1981], notes 18 and 120(9).
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