Cohen \(\cal M40(\kappa)\): Pincus' Model IV | Historical notes
Description: The ground model \(\cal M\), is a model of \(ZF +\) the class form of \(AC\)
Parameter(s): This model depends on the following parameter(s): \(\alpha\), \(\alpha\): where \(\kappa = \aleph_{\alpha}\) is a regular cardinal \(> \aleph_{0}\) and \(2^{\kappa} = \kappa^+\)
All Forms Known to be True in \(\cal M40(\kappa)\):
423,
421,
420,
419,
418,
412,
411,
410,
406,
404,
401,
390,
389,
388,
387,
386,
385,
380,
379,
378,
377,
376,
375,
374-n,
373-n,
371,
370,
362,
361,
358,
357,
356,
355,
354,
353,
352,
351,
350,
349,
345,
344,
343,
342-n,
341,
340,
339,
338,
336-n,
332,
331,
330,
329,
327,
326,
325,
324,
323,
314,
313,
311,
309,
308-p,
304,
298,
296,
295,
294,
293,
288-n,
287,
285,
283,
282,
280,
279,
276,
271-n,
270,
269,
268,
250,
249,
243,
242,
241,
235,
233,
231,
229,
228,
227,
226,
225,
223,
222,
221,
217,
216,
213,
211,
209,
206,
201,
199(\(n\)),
198,
196-alpha,
194,
185,
183-alpha,
182,
178-n-N,
174-alpha,
167,
165,
155,
154,
153,
151,
150,
146,
142,
141,
140,
139,
137-k,
132,
131,
128,
127,
126,
124,
123,
122,
121,
120-K,
119,
113,
111,
108,
107,
106,
104,
102,
99,
98,
96,
94,
93,
88,
87-alpha,
86-alpha,
85,
84,
83,
82,
80,
78,
77,
74,
73,
72,
71-alpha,
70,
69,
64,
63,
62,
61,
60,
57,
52,
49,
48-K,
47-n,
46-K,
45-n,
43,
42,
38,
35,
34,
33-n,
32,
31,
30,
29,
27,
26,
24,
19,
18,
17,
16,
14,
13,
12,
11,
10,
9,
8,
6,
5,
0,
All Forms Known to be False in \(\cal M40(\kappa)\):
430-p,
427,
391,
384,
335-n,
334,
333,
292,
286,
264,
261,
259,
256,
253,
239,
218,
214,
202,
179-epsilon,
164,
163,
152,
149,
147,
144,
133,
114,
112,
109,
95-F,
91,
90,
89,
67,
66,
51,
28-p,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 60-87-295-345
Falses that are implied by others list: 51-91-144-152-163-253-286-384
References for models trues falses list: References Pincus [1977a],\cite{1977b}, \cite{1997}, Brunner [1982a],Herrlich/Steprans [1997], Morris [1969], notes 18,120(26, 28, 34, 43, 45, and 59) and 121.
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