Fraenkel \(\cal N26\): Brunner/Pincus Model, a variation of \(\cal N2\) | Historical notes
Description: The set ofatoms \(A=\bigcup_{n\in\omega} P_n\), where the \(P_n\)'s are pairwisedisjoint denumerable sets; \(\cal G\) is the set of all permutations\(\sigma\) on \(A\) such that \(\sigma(P_n)=P_n\), for all \(n\in\omega\); and \(S\)is the set of all finite subsets of \(A\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N26\):
423,
421,
420,
419,
389,
380,
374-n,
373-n,
371,
369,
368,
367,
366,
364,
363,
362,
361,
358,
357,
352,
350,
342-n,
341,
340,
338,
337,
330,
327,
324,
316,
315,
313,
309,
307,
306,
305,
294,
289,
288-n,
280,
273,
272,
252,
251,
250,
249,
231,
223,
222,
221,
216,
212,
211,
209,
208,
207-alpha,
206,
203,
199(\(n\)),
197,
194,
191,
190,
189,
185,
182,
170,
169,
165,
151,
145,
142,
139,
137-k,
133,
132,
130,
122,
119,
118,
111,
108,
104,
94,
93,
92,
91,
90,
84,
80,
79,
77,
74,
73,
70,
63,
58,
51,
48-K,
47-n,
38,
37,
35,
34,
32,
31,
27,
26,
25,
24,
23,
19,
18,
16,
13,
10,
6,
5,
0,
All Forms Known to be False in \(\cal N26\):
430-p,
427,
426,
409,
408,
407,
399,
398,
391,
388,
387,
384,
379,
378,
377,
376,
359,
355,
347,
346,
345,
344,
343,
336-n,
335-n,
334,
333,
332,
331,
328,
326,
323,
322,
317,
303,
296,
295,
286,
284,
270,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
218,
215,
214,
213,
202,
201,
193,
192,
188,
181,
174-alpha,
168,
167,
161,
152,
149,
131,
129,
126,
123,
113,
109,
107,
106,
101,
100,
95-F,
88,
87-alpha,
86-alpha,
85,
83,
82,
76,
71-alpha,
68,
67,
66,
64,
62,
61,
60,
57,
50,
49,
45-n,
44,
43,
41,
40,
39,
36,
30,
28-p,
20,
15,
14,
12,
11,
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: 16-23-24-133-191-380
Falses that are implied by others list: 64-131-167-355
References for models trues falses list: ReferencesBrunner [1982a], De la Cruz/Di Prisco [1998a],Pincus [1976], notes 2(8,9), 18, and 120(56).
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