Cohen \(\cal M6\): Sageev's Model I | Historical notes
Description: Using iterated forcing, Sageev constructs \(\cal M6\) by adding a denumerable number of generic tree-like structuresto the ground model, a model of \(ZF + V = L\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal M6\):
423,
405,
404,
401,
390,
389,
387,
378,
377,
376,
374-n,
373-n,
358,
342-n,
336-n,
327,
325,
308-p,
304,
296,
295,
293,
288-n,
285,
283,
280,
276,
269,
268,
250,
249,
217,
216,
204,
199(\(n\)),
198,
186,
185,
182,
178-n-N,
170,
167,
146,
142,
140,
132,
128,
127,
124,
122,
121,
120-K,
111,
108,
104,
102,
98,
93,
88,
84,
83,
82,
80,
75,
73,
64,
62,
61,
57,
53,
48-K,
47-n,
46-K,
45-n,
38,
34,
33-n,
30,
19,
18,
17,
13,
12,
11,
10,
9,
4,
3,
0,
All Forms Known to be False in \(\cal M6\):
430-p,
427,
426,
424,
421,
407,
397,
396,
395,
394,
393,
392,
391,
388,
359,
354,
352,
347,
346,
345,
338,
337,
335-n,
334,
333,
330,
329,
328,
302,
292,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
231,
218,
213,
212,
211,
203,
202,
193,
192,
188,
181,
174-alpha,
168,
165,
164,
163,
150,
149,
147,
133,
130,
126,
114,
113,
112,
109,
106,
101,
100,
95-F,
94,
92,
91,
90,
89,
87-alpha,
86-alpha,
85,
79,
67,
66,
60,
51,
44,
43,
40,
39,
32,
31,
29,
28-p,
27,
23,
21,
20,
16,
8,
6,
5,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 3-34-170-295
Falses that are implied by others list: 5-163-330
References for models trues falses list: References Sageev [1975], Gonzalez [1995a],Howard/Keremedis/Rubin/Stanley/Tachtsis [1999], notes 2(8),120(9), and 123.
Back