Cohen \(\cal M25\): Freyd's Model | Historical notes
Description: Using topos-theoretic methods due to Fourman, Freyd constructs a Boolean-valued model of \(ZF\) in which every well ordered family of sets has a choice function (Form 40 is true), but \(C(|\Bbb R|,\infty)\) (Form 181) is false
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M25\):
423,
421,
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,
337,
336-n,
330,
328,
327,
325,
324,
322,
304,
296,
294,
288-n,
282,
279,
250,
249,
243,
231,
217,
216,
211,
209,
208,
199(\(n\)),
198,
196-alpha,
194,
185,
182,
170,
167,
165,
155,
154,
151,
150,
132,
131,
128,
127,
126,
124,
122,
119,
113,
111,
108,
106,
104,
98,
94,
93,
92,
86-alpha,
84,
83,
82,
80,
78,
77,
74,
73,
64,
58,
57,
48-K,
47-n,
43,
42,
40,
39,
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 \(\cal M25\):
430-p,
427,
391,
335-n,
334,
333,
292,
264,
239,
218,
214,
202,
181,
164,
163,
152,
149,
147,
133,
114,
112,
109,
95-F,
91,
90,
89,
67,
66,
28-p,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 40
Falses that are implied by others list: 91-152-163-181
References for models trues falses list: References Freyd [1980], Fourman [1980], MacLane [1971], Johnston [1984], Brunner [1982a], notes18 and 120(24, 41, and 46).
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