Cohen \(\cal M32\): Sageev's Model II | Historical notes

Description: Starting with a model \(\cal M\) of \(ZF + V =L\), Sageev constructs a sequence of models \(\cal M\subseteq N_0 \subseteq N_1\subseteq\cdots\subseteq N_{\kappa}\) where \(\kappa\) is an inaccessible cardinal, \(N_0\) is Cohen's model \(\cal M1\), and \(N_{\kappa}\) is \(\cal M32\)

Parameter(s): This model does not depend on parameters

All Forms Known to be True in \(\cal M32\):
423, 401, 390, 389, 387, 378, 377, 374-n, 373-n, 358, 342-n, 336-n, 327, 308-p, 293, 288-n, 285, 283, 280, 276, 269, 268, 250, 249, 216, 198, 178-n-N, 146, 142, 140, 132, 127, 122, 121, 120-K, 111, 102, 93, 88, 83, 80, 73, 64, 62, 61, 57, 48-K, 47-n, 46-K, 45-n, 33-n, 30, 18, 12, 11, 10, 0,

All Forms Known to be False in \(\cal M32\):
430-p, 427, 426, 407, 391, 388, 359, 347, 346, 345, 335-n, 334, 333, 328, 292, 286, 264, 262, 261, 260, 259, 258, 257, 256, 255, 239, 218, 214, 202, 193, 192, 188, 181, 174-alpha, 168, 164, 161, 152, 149, 147, 133, 129, 126, 114, 113, 112, 109, 106, 101, 100, 95-F, 91, 90, 89, 87-alpha, 86-alpha, 71-alpha, 67, 66, 44, 43, 41, 40, 39, 28-p, 20, 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: 30-57

Falses that are implied by others list: 9-91-126

References for models trues falses list: References Sageev [1981], notes 18 and 120(9).

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