Cohen \(\cal M7\): Cohen's Second Model | Historical notes
Description: There are two denumerable subsets\(U=\{U_i:i\in\omega\}\) and \(V=\{V_i:i\in\omega\}\) of \(\cal P({\Bbb R})\)(neither of which is in the model) such that for each \(i\in\omega\), \(U_i\)and \(V_i\) cannot be distinguished in the model
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M7\):
191,
190,
189,
182,
0,
All Forms Known to be False in \(\cal M7\):
430-p,
427,
426,
422-n,
421,
412,
411,
410,
409,
408,
407,
406,
403,
402,
401,
400,
399,
398,
394,
393,
392,
391,
389,
386,
385,
384,
380,
379,
378,
377,
376,
359,
358,
355,
354,
352,
347,
346,
345,
344,
343,
341,
340,
338,
335-n,
334,
333,
332,
331,
327,
326,
325,
324,
323,
322,
317,
303,
302,
295,
292,
286,
284,
270,
264,
262,
261,
260,
259,
258,
257,
256,
255,
250,
239,
231,
218,
214,
213,
202,
201,
192,
181,
174-alpha,
168,
167,
166,
165,
164,
161,
154,
153,
152,
151,
150,
149,
147,
139,
133,
132,
130,
129,
123,
122,
121,
114,
113,
112,
111,
110,
109,
107,
101,
100,
95-F,
91,
90,
89,
88,
87-alpha,
86-alpha,
85,
80,
79,
71-alpha,
68,
67,
66,
62,
61,
60,
50,
49,
44,
43,
41,
40,
39,
36,
32,
31,
30,
29,
28-p,
27,
23,
21,
20,
18,
17,
16,
15,
14,
10,
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: 191
Falses that are implied by others list: 18-389
References for models trues falses list: ReferencesBlass [1979], Cohen [1965], \cite{1963}, \cite{1966},Good/Tree [1995], Jech [1973b] (pp 68ff), and Note 18.
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