Cohen \(\cal M30\): Pincus/Solovay Model II | Historical notes
Description: In this construction, an \(\omega_1\) sequence of generic reals is added to a model of \(ZFC\) in such a way that the Principle of Dependent Choices (Form 43) is true, but no nonprincipal measure exists (Form 223 is false)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M30\):
423,
420,
419,
418,
412,
411,
404,
390,
389,
388,
387,
380,
379,
378,
377,
376,
375,
374-n,
373-n,
362,
361,
358,
357,
355,
354,
353,
352,
351,
350,
342-n,
341,
340,
339,
338,
336-n,
325,
312,
304,
296,
288-n,
282,
279,
253,
249,
243,
217,
216,
211,
209,
199(\(n\)),
198,
194,
185,
182,
167,
155,
154,
150,
132,
131,
128,
127,
126,
124,
119,
113,
108,
106,
104,
98,
94,
84,
83,
82,
80,
78,
77,
74,
73,
64,
57,
43,
42,
38,
35,
34,
32,
31,
29,
27,
26,
24,
19,
18,
17,
16,
13,
12,
11,
10,
9,
8,
6,
5,
0,
All Forms Known to be False in \(\cal M30\):
430-p,
427,
407,
391,
385,
384,
345,
335-n,
334,
333,
317,
313,
311,
303,
292,
287,
264,
239,
225,
223,
222,
221,
218,
206,
202,
164,
163,
149,
147,
133,
130,
123,
114,
112,
109,
99,
95-F,
91,
90,
89,
79,
70,
67,
66,
63,
52,
50,
28-p,
14,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 43-253-312
Falses that are implied by others list: 163-223
References for models trues falses list: References Pincus/Solovay [1977], Brunner [1982a],Howard [1975], and Wagon [1985].
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