Cohen \(\cal M3\): Mathias' model | Historical notes
Description: Mathias proves that the \(FM\) model \(\cal N4\) can be transformed into a model of \(ZF\), \(\cal M3\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M3\):
423,
421,
404,
401,
390,
389,
387,
380,
379,
378,
377,
376,
374-n,
373-n,
358,
357,
356,
355,
350,
349,
342-n,
338,
336-n,
330,
329,
327,
324,
323,
322,
314,
308-p,
296,
295,
294,
293,
288-n,
285,
283,
280,
276,
271-n,
270,
269,
268,
250,
249,
231,
216,
213,
198,
178-n-N,
167,
165,
151,
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,
60,
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 \(\cal M3\):
430-p,
427,
407,
391,
384,
345,
335-n,
334,
333,
317,
303,
292,
264,
239,
218,
214,
202,
179-epsilon,
164,
152,
149,
147,
144,
133,
114,
112,
109,
99,
95-F,
91,
90,
89,
67,
66,
50,
49,
28-p,
14,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 15-60
Falses that are implied by others list: 49-91-99-144-152
References for models trues falses list: References Mathias [1967], notes 25, 33 and 120(6, 34 and43). Also, see Felgner [1971a] (pp 114--128) and Jech [1973b] (p 113, prob 8).
Back