Cohen \(\cal M29\): Pincus' Model II | Historical notes
Description: Pincus constructs a generic extension \(M[I]\) of a model \(M\) of \(ZF +\) class choice \(+ GCH\) in which \(I=\bigcup_{n\in\omega}I_n\), \(I_{-1}=2\) and \(I_{n+1}\) is a denumerable set of independent functions from \(\omega\) onto \(I_n\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M29\):
425,
423,
405,
404,
401,
390,
389,
387,
378,
377,
376,
374-n,
373-n,
358,
342-n,
336-n,
327,
325,
308-p,
304,
296,
295,
293,
291,
290,
288-n,
285,
283,
280,
276,
269,
268,
250,
249,
217,
216,
214,
200,
199(\(n\)),
198,
185,
178-n-N,
173,
167,
152,
146,
142,
140,
132,
131,
128,
127,
124,
122,
121,
120-K,
111,
102,
98,
93,
88,
84,
83,
82,
80,
76,
75,
73,
64,
62,
61,
57,
48-K,
47-n,
46-K,
45-n,
33-n,
30,
18,
17,
13,
12,
11,
10,
9,
4,
0,
All Forms Known to be False in \(\cal M29\):
430-p,
427,
426,
421,
407,
403,
402,
400,
399,
398,
397,
396,
395,
394,
393,
392,
391,
388,
359,
357,
356,
355,
354,
353,
352,
351,
350,
349,
347,
346,
345,
338,
335-n,
334,
333,
330,
329,
328,
324,
323,
322,
302,
292,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
231,
218,
213,
202,
193,
192,
188,
181,
174-alpha,
168,
165,
164,
163,
151,
150,
149,
147,
133,
126,
118,
115,
114,
113,
112,
109,
106,
101,
100,
95-F,
91,
90,
89,
87-alpha,
86-alpha,
85,
67,
66,
60,
44,
43,
40,
39,
32,
31,
29,
28-p,
27,
23,
21,
20,
16,
15,
8,
3,
2,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 200-214-290-291-295
Falses that are implied by others list: 3-91-118-151-163-350-357
References for models trues falses list: References Pincus [1974a],\cite{1978}, \cite{1997}, Brunner [1982a], notes 18, 64, and120(16 and 43).
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