Cohen \(\cal M34(\aleph_1)\): Pincus' Model III | Historical notes
Description: Pincus proves that Cohen's model \(\cal M1\) can be extended by adding \(\aleph_1\) generic sets along with the set \(b\) containing them and well orderings of all countable subsets of \(b\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M34(\aleph_1)\):
423,
404,
401,
390,
389,
387,
379,
378,
377,
376,
374-n,
373-n,
358,
357,
356,
355,
350,
349,
342-n,
336-n,
327,
324,
323,
322,
314,
308-p,
296,
295,
293,
288-n,
285,
283,
280,
276,
271-n,
270,
269,
268,
250,
249,
216,
198,
178-n-N,
167,
150,
146,
142,
140,
132,
127,
122,
121,
120-K,
119,
111,
108,
102,
93,
88,
85,
84,
83,
82,
80,
73,
64,
62,
61,
48-K,
47-n,
46-K,
45-n,
38,
33-n,
32,
30,
18,
15,
12,
11,
10,
5,
0,
All Forms Known to be False in \(\cal M34(\aleph_1)\):
430-p,
427,
397,
396,
395,
394,
393,
392,
391,
359,
347,
335-n,
334,
333,
330,
329,
328,
302,
292,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
231,
218,
213,
202,
168,
165,
164,
163,
149,
147,
133,
114,
112,
109,
101,
100,
95-F,
91,
90,
89,
67,
66,
60,
40,
28-p,
20,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 15-85
Falses that are implied by others list: 91-163-213-330
References for models trues falses list: References Pincus [1977a], notes 74 and 120(6 and 30).
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