Cohen \(\cal M1\): Cohen's original model | Historical notes
Description: Add a denumerable number of generic reals (subsets of \(\omega\)), \(a_1\), \(a_2\), \(\cdots\), along with the set \(b\) containing them
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M1\):
423,
421,
420,
419,
412,
411,
410,
406,
404,
401,
390,
389,
387,
386,
385,
380,
379,
378,
377,
376,
374-n,
373-n,
371,
370,
358,
357,
356,
355,
350,
349,
344,
343,
342-n,
338,
336-n,
332,
331,
330,
329,
327,
326,
324,
323,
322,
314,
313,
311,
309,
308-p,
298,
296,
295,
294,
293,
288-n,
287,
285,
283,
280,
277,
276,
271-n,
270,
269,
268,
250,
249,
242,
241,
235,
233,
231,
229,
228,
227,
226,
225,
223,
222,
221,
216,
213,
209,
206,
201,
198,
191,
190,
189,
182,
178-n-N,
170,
167,
165,
163,
154,
153,
151,
150,
146,
142,
141,
140,
139,
137-k,
132,
128,
127,
123,
122,
121,
120-K,
119,
118,
111,
108,
107,
104,
102,
99,
96,
93,
88,
85,
84,
83,
82,
80,
73,
72,
70,
69,
64,
63,
62,
61,
60,
52,
49,
48-K,
47-n,
46-K,
45-n,
38,
35,
34,
33-n,
32,
31,
30,
19,
18,
15,
14,
12,
11,
10,
6,
5,
0,
All Forms Known to be False in \(\cal M1\):
430-p,
427,
426,
424,
407,
394,
392,
391,
388,
369,
359,
347,
346,
345,
337,
335-n,
334,
333,
328,
325,
316,
303,
302,
301,
300,
299,
297,
292,
289,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
253,
239,
218,
214,
212,
211,
203,
202,
193,
192,
188,
185,
181,
179-epsilon,
175,
174-alpha,
168,
164,
161,
152,
149,
147,
144,
133,
131,
130,
129,
126,
114,
113,
112,
109,
106,
101,
100,
95-F,
94,
92,
91,
90,
89,
87-alpha,
86-alpha,
79,
77,
76,
71-alpha,
67,
66,
65,
51,
50,
44,
43,
41,
40,
39,
28-p,
20,
17,
16,
13,
9,
8,
7,
4,
3,
2,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 14-15-31-60-118-128-163-170-191-277
Falses that are implied by others list: 13-17-50-65-131-144-253-289-299-300-369
References for models trues falses list: References include Bell [1983], \cite{1988},Blass [1979], \cite{1977a}, Brunner [1982a],\cite{1984b}, \cite{1984f}, Cohen [1963], \cite{1966},David [1980], Good/Tree [1995], Halpern/Levy [1971], Haddad/Morillon [1990], Howard [1975],Howard/Keremedis/Rubin/Stanley/Tachtsis [1999], Monro [1972], \cite{1973a}, Sageev [1981], Shoenfield [1967], Smullyan [1994] and Note 120(30 and 49). See,also, Felgner [1971a] (pp 100--103, 131--145), and Jech [1973b] (Chapt.~5, probs 20, 22).
Back