Fraenkel \(\cal N50(E)\): Brunner's Model III | Historical notes
Description: \(E\) is a finite set of prime numbers.For each \(p\in E\) and \(n\in\omega\), let \(A_{p,n}\) be a set of atoms ofcardinality \(p^n\)
Parameter(s): This model depends on the following parameter(s): \(E\), \(E\): finite set of prime numbers
All Forms Known to be True in \(\cal N50(E)\):
425,
423,
420,
419,
418,
416,
415,
414,
413,
397,
396,
395,
390,
389,
387,
382,
381,
375,
374-n,
373-n,
371,
369,
368,
367,
366,
364,
363,
362,
361,
358,
357,
355,
350,
349,
337,
330,
329,
328,
327,
324,
322,
316,
315,
313,
309,
307,
306,
305,
294,
292,
289,
288-n,
287,
280,
273,
272,
254,
252,
251,
250,
232,
223,
222,
221,
212,
211,
208,
206,
203,
199(\(n\)),
197,
194,
191,
190,
189,
185,
182,
173,
170,
169,
155,
147,
145,
144,
142,
139,
137-k,
131,
130,
127,
126,
125,
119,
118,
116,
115,
114,
112,
111,
108,
106,
104,
94,
93,
92,
91,
90,
89,
84,
83,
82,
80,
79,
78,
77,
76,
74,
70,
67,
64,
58,
52,
51,
48-K,
47-n,
38,
37,
35,
34,
25,
19,
18,
13,
6,
5,
0,
All Forms Known to be False in \(\cal N50(E)\):
426,
421,
412,
411,
410,
409,
408,
407,
406,
399,
394,
393,
392,
391,
386,
385,
384,
380,
379,
378,
377,
376,
359,
354,
352,
347,
345,
344,
343,
342-n,
341,
340,
338,
332,
331,
325,
323,
317,
303,
302,
295,
286,
284,
270,
264,
262,
261,
260,
259,
258,
257,
256,
255,
231,
218,
214,
213,
202,
192,
181,
174-alpha,
168,
165,
164,
161,
154,
153,
152,
151,
150,
133,
132,
129,
123,
122,
121,
113,
109,
107,
101,
100,
87-alpha,
86-alpha,
85,
73,
71-alpha,
68,
62,
61,
60,
50,
49,
45-n,
44,
43,
41,
40,
39,
36,
32,
31,
30,
29,
27,
23,
21,
20,
17,
16,
15,
14,
12,
11,
10,
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: 67-191-322
Falses that are implied by others list: 10-164-342
References for models trues falses list: References Brunner [1990], notes 18 and 120(2, 10, and 56).
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