Cohen \(\cal M7(n)\): Generalization of \(\cal M7\) | Historical notes
Description: Model \(\cal M7\) can be generalized to \(n\) denumerable sets for \(1 \le n \in\omega\), then the Axiom of Choice for a denumerable number of \(n\) element sets, \(C(\aleph_0,n)\), is false for \(1 \le n \le \omega\)
Parameter(s): This model depends on the following parameter(s): \(n\), \(n\): integer \(> 1\)
All Forms Known to be True in \(\cal M7(n)\):
0,
All Forms Known to be False in \(\cal M7(n)\):
430-p,
427,
422-n,
409,
408,
407,
403,
402,
401,
400,
399,
398,
394,
393,
392,
391,
384,
359,
347,
345,
344,
343,
335-n,
334,
333,
332,
331,
327,
324,
323,
322,
317,
303,
302,
295,
292,
286,
284,
270,
264,
262,
261,
260,
259,
258,
257,
256,
255,
250,
239,
231,
218,
213,
202,
168,
165,
164,
151,
149,
147,
133,
123,
122,
121,
114,
112,
109,
107,
101,
100,
95-F,
91,
90,
89,
85,
68,
67,
66,
62,
61,
60,
50,
49,
47-n,
45-n,
40,
36,
33-n,
30,
28-p,
23,
21,
20,
15,
14,
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: 47-91
References for models trues falses list: Reference Note 18.
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