Fraenkel \(\cal N43\): Brunner's Model II | Historical notes
Description: The set of atoms \(A=\bigcup\{P_n: n\in\omega\}\), where \(|P_n|=n+1\) for each \(n\in\omega\) and the \(P_n\)'s arepairwise disjoint
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N43\):
389,
371,
369,
368,
367,
366,
364,
363,
362,
361,
313,
309,
307,
306,
305,
289,
280,
273,
272,
252,
251,
223,
222,
212,
211,
206,
203,
199(\(n\)),
197,
194,
191,
190,
189,
182,
170,
169,
145,
142,
139,
137-k,
130,
108,
104,
94,
93,
92,
91,
79,
74,
70,
38,
37,
35,
34,
19,
13,
6,
5,
0,
All Forms Known to be False in \(\cal N43\):
430-p,
427,
426,
422-n,
421,
412,
411,
410,
409,
408,
407,
406,
403,
402,
401,
400,
399,
398,
394,
393,
392,
391,
388,
387,
386,
385,
384,
380,
378,
377,
376,
359,
358,
355,
354,
352,
347,
346,
345,
344,
343,
341,
340,
338,
336-n,
335-n,
334,
333,
332,
331,
328,
327,
326,
325,
324,
323,
322,
317,
303,
302,
296,
295,
286,
284,
270,
264,
262,
261,
260,
259,
258,
257,
256,
255,
250,
239,
231,
218,
215,
214,
213,
202,
201,
193,
192,
188,
181,
174-alpha,
168,
165,
161,
154,
153,
152,
151,
150,
149,
133,
132,
129,
126,
123,
122,
121,
113,
111,
110,
109,
107,
106,
101,
100,
95-F,
88,
87-alpha,
86-alpha,
85,
83,
82,
80,
71-alpha,
68,
67,
66,
64,
62,
61,
60,
57,
50,
49,
45-n,
44,
43,
41,
40,
39,
36,
32,
31,
30,
29,
28-p,
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: 91-191
Falses that are implied by others list: 64-80
References for models trues falses list: References Brunner [1986], notes 18, 120(56), and 122.
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