Cohen \(\cal M46(m,M)\): Pincus' Model VIII | Historical notes

Description: This model depends on the natural number \(m\) and the set of natural numbers \(M\) which must satisfy Mostowski's condition:

  • \(S(M,m)\): For everydecomposition \(m = p_{1} + \ldots + p_{s}\) of \(m\) into a sum of primes at least one \(p_{i}\) divides an element of \(M\)

Parameter(s): This model depends on the following parameter(s): \(M\), \(M\): finite subset of natural numbers

All Forms Known to be True in \(\cal M46(m,M)\):
425, 423, 420, 419, 418, 412, 411, 405, 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, 279, 249, 243, 217, 216, 214, 211, 209, 199(\(n\)), 198, 194, 185, 182, 173, 167, 155, 154, 152, 150, 132, 131, 128, 127, 126, 124, 120-K, 119, 113, 108, 106, 104, 98, 94, 84, 83, 82, 80, 78, 77, 76, 75, 74, 73, 64, 57, 48-K, 46-K, 43, 42, 38, 35, 34, 32, 31, 29, 27, 26, 24, 19, 18, 17, 16, 13, 12, 11, 10, 9, 8, 6, 5, 4, 0,

All Forms Known to be False in \(\cal M46(m,M)\):
430-p, 427, 409, 408, 407, 399, 391, 384, 359, 347, 345, 344, 343, 335-n, 334, 333, 332, 331, 329, 323, 317, 303, 295, 292, 286, 284, 270, 264, 262, 261, 260, 259, 258, 257, 256, 255, 239, 231, 218, 213, 202, 168, 164, 163, 151, 149, 147, 133, 123, 114, 112, 109, 107, 101, 100, 95-F, 91, 90, 89, 85, 68, 67, 66, 62, 61, 60, 50, 49, 45-n, 40, 36, 30, 28-p, 23, 21, 20, 15, 14, 1,

A minimial list of forms whose truth in this model imply all others that are true in this model: 43-46-214

Falses that are implied by others list: 45-91-151-163-329

References for models trues falses list: References Pincus [1974b], \cite{1977a},notes 18 and 120(1, 4, 43, and 48).

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