Fraenkel \(\cal N41\): Another variation of \(\cal N3\) | Historical notes
Description: \(A=\bigcup\{B_n; n\in\omega\}\)is a disjoint union, where each \(B_n\) is denumerable and ordered like therationals by \(\le_n\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N41\):
423,
416,
415,
414,
413,
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,
327,
325,
313,
309,
307,
306,
305,
304,
296,
289,
288-n,
280,
273,
272,
252,
251,
250,
249,
223,
222,
221,
217,
216,
212,
211,
206,
203,
199(\(n\)),
198,
197,
194,
191,
190,
189,
185,
182,
170,
169,
167,
145,
144,
142,
139,
137-k,
132,
130,
128,
127,
125,
124,
122,
111,
108,
104,
98,
94,
93,
92,
91,
84,
83,
82,
80,
79,
74,
73,
70,
64,
63,
57,
48-K,
47-n,
38,
37,
35,
34,
19,
18,
17,
13,
12,
11,
10,
9,
6,
5,
0,
All Forms Known to be False in \(\cal N41\):
430-p,
427,
426,
421,
409,
408,
407,
403,
402,
400,
399,
398,
397,
396,
395,
394,
393,
392,
391,
388,
384,
359,
357,
356,
355,
354,
353,
352,
351,
350,
349,
347,
346,
345,
344,
343,
338,
335-n,
334,
333,
332,
331,
330,
329,
328,
326,
324,
323,
322,
317,
303,
302,
295,
294,
292,
286,
284,
270,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
231,
218,
213,
202,
201,
193,
192,
188,
181,
174-alpha,
168,
165,
163,
150,
149,
133,
126,
123,
114,
113,
112,
109,
107,
106,
101,
100,
95-F,
90,
89,
88,
87-alpha,
86-alpha,
85,
68,
67,
66,
62,
61,
60,
51,
50,
49,
44,
43,
40,
39,
36,
32,
31,
30,
29,
28-p,
27,
23,
21,
20,
16,
15,
14,
8,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 9-63-91-122-144-191
Falses that are implied by others list: 88-163-294-350-357
References for models trues falses list: References De la Cruz, Hall, Howard, Keremedis, Rubin [2002a] notes 18, 112, 120(56), 123, and 155.
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