Fraenkel \(\cal N8\): L\"auchli's Model II | Historical notes
Description: \(A\) is countably infinite, ordered likethe rational numbers; \(\cal G\) is the group of all order automorphisms of\(A\); and \(S\) is the set of all subsets \(E\) of \(A\) such that \(E\) has atmost a finite number of accumulation points and every infinite subset of\(E\) has an accumulation point
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N8\):
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 \(\cal N8\):
430-p,
427,
407,
388,
375,
359,
347,
345,
335-n,
334,
333,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
218,
202,
193,
192,
188,
174-alpha,
168,
149,
109,
106,
101,
100,
95-F,
87-alpha,
78,
67,
66,
44,
43,
40,
28-p,
20,
15,
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: 15-78
References for models trues falses list: References L\"auchli [1962],Jech/Sochor [1966a], and Note 18.
Back