Fraenkel \(\cal N24(n)\): An extension of \(\cal N24\) to \(n\)-element sets, \(n>1\).\(A=\bigcup B\), where \( B=\{b_i: i\in\omega\}\) is a pairwise disjoint setof \(n\)-element sets | Historical notes
Description: \(\cal G\) is the group of all permutations of \(A\)which are permutations of \(B\); and \(S\) is the set of all finite subsets of\(A\)
Parameter(s): This model depends on the following parameter(s): \(n\), \(n\): integer \(>\) 1
All Forms Known to be True in \(\cal N24(n)\):
423,
421,
420,
419,
401,
389,
374-n,
373-n,
371,
369,
368,
367,
366,
364,
363,
362,
361,
358,
357,
352,
350,
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,
130,
122,
121,
120-K,
119,
118,
111,
108,
104,
94,
93,
92,
91,
90,
84,
80,
79,
77,
74,
70,
63,
58,
51,
48-K,
47-n,
38,
37,
35,
34,
33-n,
32,
31,
27,
26,
25,
24,
23,
19,
18,
16,
13,
10,
6,
5,
0,
All Forms Known to be False in \(\cal N24(n)\):
430-p,
427,
426,
409,
408,
407,
399,
391,
388,
387,
384,
378,
377,
376,
359,
347,
346,
345,
344,
343,
336-n,
335-n,
334,
333,
332,
331,
328,
326,
323,
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,
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: 16-23-24-121-133-191
Falses that are implied by others list: 64-131
References for models trues falses list: References Brunner [1982a], Hickman [1976], Truss [1973a], notes 2(8,9), 18, and 120(49 and 56).
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