Fraenkel \(\cal N13\): L\"auchli/Jech Model | Historical notes
Description: \(A = B_1\cup B_2\), where \(B_1=\bigcup\{A_{j1} : j\in\omega\}\), and \(B_2 = \bigcup\{A_{j2} :j\in\omega\}\), and each \(A_{ji}\) is a 6-element set
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N13\):
389,
371,
369,
368,
367,
366,
364,
363,
362,
361,
313,
309,
307,
306,
305,
289,
280,
273,
272,
252,
251,
223,
222,
212,
211,
206,
203,
199(\(n\)),
197,
194,
191,
190,
189,
182,
170,
169,
145,
142,
139,
137-k,
130,
108,
104,
94,
93,
92,
91,
79,
74,
70,
38,
37,
35,
34,
19,
13,
6,
5,
0,
All Forms Known to be False in \(\cal N13\):
426,
407,
384,
359,
347,
345,
317,
303,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
235,
214,
202,
192,
181,
174-alpha,
168,
161,
152,
129,
113,
107,
101,
100,
96,
87-alpha,
86-alpha,
71-alpha,
50,
44,
43,
41,
40,
39,
20,
15,
14,
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: 91-191
Falses that are implied by others list: 9-15-235
References for models trues falses list: References L\"auchli [1962], Jech/Sochor [1966a], Jech [1973b] (p 149prob 5), and Note 18.
Back