Cohen \(\cal M38\): Shelah's Model II | Historical notes
Description: In a model of \(ZFC +\) "\(\kappa\) is a strongly inaccessible cardinal", Shelah uses Levy's method of collapsing cardinals to collapse \(\kappa\) to \(\aleph_1\) similarly to Solovay [1970]
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M38\):
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,
280,
279,
249,
243,
217,
216,
211,
209,
199(\(n\)),
198,
194,
185,
182,
169,
167,
155,
154,
150,
142,
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 \(\cal M38\):
430-p,
427,
409,
408,
407,
399,
394,
392,
391,
385,
384,
368,
367,
366,
363,
359,
347,
345,
344,
343,
337,
335-n,
334,
333,
332,
331,
326,
323,
317,
309,
306,
305,
303,
302,
295,
292,
286,
284,
270,
264,
262,
261,
260,
259,
258,
257,
256,
255,
252,
251,
239,
225,
218,
213,
203,
202,
201,
195,
184,
170,
168,
164,
163,
149,
147,
133,
130,
123,
114,
112,
109,
107,
101,
100,
99,
95-F,
93,
92,
91,
90,
89,
88,
85,
79,
70,
68,
67,
66,
63,
62,
61,
60,
52,
51,
50,
49,
40,
36,
30,
28-p,
20,
15,
14,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 43-142-169
Falses that are implied by others list: 93-163
References for models trues falses list: ReferencesShelah [1985], Solovay [1970], and Brunner [1982a].
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