Fraenkel \(\cal N57\): The set of atoms \(A=\cup\{A_{n}:n\in\aleph_{1}\}\), where\(A_{n}=\{a_{nx}:x\in B(0,1)\}\) and \(B(0,1)\) is the set of points on theunit circle centered at 0 | Historical notes
Description: The group of permutations \(\cal{G}\) is thegroup of all permutations on \(A\) which rotate the \(A_{n}\)'s by an angle\(\theta_{n}\in\Bbb{R}\) and supports are countable
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N57\):
423,
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,
336-n,
325,
304,
296,
288-n,
282,
279,
249,
243,
217,
216,
211,
209,
199(\(n\)),
198,
194,
185,
182,
167,
155,
154,
150,
132,
131,
128,
127,
126,
124,
119,
113,
108,
106,
104,
98,
94,
84,
83,
82,
80,
78,
77,
74,
73,
64,
57,
43,
42,
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 \(\cal N57\):
430-p,
427,
426,
382,
381,
335-n,
334,
333,
239,
232,
218,
214,
173,
149,
109,
95-F,
76,
67,
66,
28-p,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 43
Falses that are implied by others list: 173-382
References for models trues falses list: References De la Cruz\slash Hall\slash howard\slash Keremedis\slashRubin [2002a].
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