Fraenkel \(\cal N21(\aleph_{\alpha+1})\): Jensen's Model | Historical notes
Description: We assume \(\aleph_{\alpha+1}\) is a regular cardinal
Parameter(s): This model depends on the following parameter(s): \(\alpha\), \(\alpha\): \(\aleph_{\alpha+1}\) a regular cardinal
All Forms Known to be True in \(\cal N21(\aleph_{\alpha+1})\):
423,
420,
419,
418,
404,
390,
389,
387,
380,
379,
378,
377,
376,
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,
338,
336-n,
325,
313,
309,
307,
306,
305,
304,
296,
289,
288-n,
282,
280,
273,
272,
252,
251,
249,
223,
222,
221,
217,
216,
212,
211,
209,
206,
203,
199(\(n\)),
198,
197,
196-alpha,
194,
191,
190,
189,
185,
183-alpha,
182,
170,
169,
167,
150,
145,
142,
139,
137-k,
132,
131,
130,
128,
127,
126,
124,
119,
108,
104,
98,
94,
93,
92,
91,
86-alpha,
84,
83,
82,
80,
79,
74,
73,
71-alpha,
70,
64,
63,
57,
39,
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 \(\cal N21(\aleph_{\alpha+1})\):
430-p,
427,
407,
388,
359,
347,
345,
335-n,
334,
333,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
218,
202,
193,
192,
188,
174-alpha,
168,
163,
149,
133,
109,
106,
101,
100,
95-F,
87-alpha,
67,
66,
44,
43,
40,
28-p,
20,
15,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 39-63-71-86-91-191
Falses that are implied by others list: 15-106-133-163
References for models trues falses list: References Jensen [1966], \cite{1967},Blass [1979], Brunner [1982a], and Note 60. See,also, Jech [1973b] (p 130) and Felgner [1971a] (pp151-159), notes 18 and 120(4 and 55).
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