Cohen \(\cal M26\): Kanovei's Model I | Historical notes
Description: Starting with a model of \(ZF + V = L\) and using forcing techniques due to Jensen [1968], Kanovei constructs a model of \(ZF\) in which there is an infinite Dedekind finite set \(A\) of generic reals that is in the class \(\varPi^1_n\), but there are no infinite Dedekind finite subsets of \(\Bbb R\) in the class \(\varSigma^1_n\), where \(n\in\omega\), \(n\ge 2\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M26\):
0,
All Forms Known to be False in \(\cal M26\):
430-p,
427,
426,
424,
407,
394,
392,
391,
388,
359,
347,
346,
345,
337,
335-n,
334,
333,
328,
316,
302,
292,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
218,
214,
212,
211,
203,
202,
199(\(n\)),
193,
192,
188,
185,
181,
175,
174-alpha,
168,
164,
161,
152,
149,
147,
133,
130,
129,
126,
114,
113,
112,
109,
106,
101,
100,
95-F,
94,
92,
91,
90,
89,
87-alpha,
86-alpha,
79,
77,
71-alpha,
67,
66,
51,
44,
43,
41,
40,
39,
28-p,
20,
16,
13,
9,
8,
7,
4,
3,
2,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 0
Falses that are implied by others list: 199
References for models trues falses list: References Kanovei [1978], Jensen [1968], and Note 61.
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