Fraenkel \(\cal N14\): Morris/Jech Model | Historical notes
Description: \(A = \bigcup\{A_{\alpha}: \alpha <\omega_1\}\), where the \(A_{\alpha}\)'s are pairwise disjoint, each iscountably infinite, and each is ordered like the rationals; \(\cal G\) isthe group of all permutations on \(A\) that leave each \(A_{\alpha}\) fixedand preserve the ordering on each \(A_{\alpha}\); and \(S = \{B_{\gamma}:\gamma < \omega_1\}\), where \(B_{\gamma}= \bigcup\{A_{\alpha}: \alpha <\gamma\}\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N14\):
423,
420,
419,
418,
416,
415,
414,
413,
412,
411,
404,
390,
389,
388,
387,
380,
379,
378,
377,
376,
375,
374-n,
373-n,
371,
369,
368,
367,
366,
364,
363,
362,
361,
358,
357,
355,
354,
353,
352,
351,
350,
342-n,
341,
340,
339,
338,
336-n,
325,
313,
309,
307,
306,
305,
304,
296,
289,
288-n,
282,
280,
279,
273,
272,
252,
251,
249,
243,
223,
222,
221,
217,
216,
212,
211,
209,
206,
203,
199(\(n\)),
198,
197,
194,
191,
190,
189,
185,
182,
170,
169,
167,
155,
154,
150,
145,
144,
142,
139,
137-k,
132,
131,
130,
128,
127,
126,
125,
124,
119,
113,
108,
106,
104,
98,
94,
93,
92,
91,
84,
83,
82,
80,
79,
78,
77,
74,
73,
70,
64,
63,
57,
43,
42,
38,
37,
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 \(\cal N14\):
192,
163,
133,
103,
15,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 43-63-91-144-191
Falses that are implied by others list: 15-103-133-163-192
References for models trues falses list: References Jech [1973b] (p 164 prob 21), notes 18, 144, 120(1,4, and 20), and 155.
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