Fraenkel \(\cal N55\): Keremedis/Tachtsis Model: The set of atoms \(A=\bigcup \{A_n: n\in \omega\}\), where \(A_n=\{a_{n,x}: x\in B(0,\frac1n)\}\) and \(B(0,\frac1n)= \{x: \rho(x,0)=\frac1n\}\), where \(\rho\) is the Euclidean metric | Historical notes
Description: The group of permutations \(\cal G\), is the group of all rotations of the \(A_n\) through an angle \(\theta\in [0,2\pi)\), and supports are finite
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N55\):
423,
404,
390,
389,
387,
378,
377,
376,
374-n,
373-n,
371,
369,
368,
367,
366,
364,
363,
362,
361,
358,
342-n,
336-n,
325,
313,
309,
307,
306,
305,
304,
296,
289,
288-n,
280,
273,
272,
252,
251,
249,
223,
222,
217,
216,
212,
211,
206,
203,
199(\(n\)),
198,
197,
194,
191,
190,
189,
185,
182,
170,
169,
167,
145,
142,
139,
137-k,
132,
130,
128,
127,
124,
108,
104,
98,
94,
93,
92,
91,
84,
83,
82,
80,
79,
74,
73,
70,
64,
57,
38,
37,
35,
34,
19,
18,
17,
13,
12,
11,
10,
9,
6,
5,
0,
All Forms Known to be False in \(\cal N55\):
430-p,
427,
426,
421,
407,
394,
393,
392,
391,
388,
384,
359,
347,
346,
345,
343,
335-n,
334,
333,
332,
331,
328,
317,
303,
302,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
231,
218,
214,
202,
193,
192,
188,
181,
174-alpha,
168,
165,
154,
149,
133,
131,
126,
123,
116,
113,
109,
106,
101,
100,
95-F,
87-alpha,
86-alpha,
76,
67,
66,
60,
50,
44,
43,
40,
39,
36,
28-p,
20,
15,
14,
8,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 9-91-191
Falses that are implied by others list: 15-116-131-154-165-421
References for models trues falses list: References Keremedis/Tachtsis [1999a], \cite {2000}and Note 18.
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