Cohen \(\cal M36\): Figura's Model | Historical notes
Description: Starting with a countable, standard model, \(\cal M\), of \(ZFC + 2^{\aleph_0}=\aleph_{\omega +1}\), Figura uses forcing conditions that are functions from a subset of \(\omega\times\omega\) to \(\omega_\omega\) to construct a symmetric extension of \(\cal M\) in which there is an uncountable well ordered subset of the reals (Form 170 is true), but \(\aleph_1= \aleph_{\omega}\) so \(\aleph_1\) is singular (Form 34 is false)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M36\):
170,
93,
0,
All Forms Known to be False in \(\cal M36\):
430-p,
427,
426,
424,
420,
419,
418,
407,
394,
392,
391,
388,
381,
359,
352,
347,
346,
345,
337,
335-n,
334,
333,
328,
302,
292,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
245,
239,
218,
212,
211,
203,
202,
193,
192,
188,
181,
174-alpha,
172,
168,
164,
149,
147,
133,
130,
126,
114,
113,
112,
109,
106,
101,
100,
95-F,
94,
92,
91,
90,
89,
87-alpha,
86-alpha,
79,
67,
66,
51,
44,
43,
40,
39,
34,
31,
29,
28-p,
27,
25,
23,
21,
20,
16,
8,
6,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 170
Falses that are implied by others list: 6-34
References for models trues falses list: References Figura [1981], Howard/Keremedis/Rubin/Stanley/Tachtsis [1999],notes 3 and 18.
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