Fraenkel \(\cal N7\): L\"auchli's Model I | Historical notes
Description: \(A\) is countably infinite
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N7\):
423,
421,
420,
419,
401,
390,
389,
380,
378,
374-n,
373-n,
371,
369,
368,
367,
366,
364,
363,
362,
361,
358,
357,
356,
352,
350,
349,
344,
343,
342-n,
338,
336-n,
332,
331,
330,
329,
327,
324,
323,
315,
314,
313,
309,
308-p,
307,
306,
305,
294,
289,
288-n,
285,
283,
280,
276,
273,
272,
271-n,
270,
269,
268,
252,
251,
250,
249,
231,
223,
222,
221,
216,
213,
212,
211,
209,
207-alpha,
206,
203,
199(\(n\)),
197,
194,
191,
190,
189,
182,
178-n-N,
170,
169,
165,
154,
151,
150,
146,
145,
142,
140,
139,
137-k,
132,
130,
127,
123,
122,
121,
120-K,
119,
111,
108,
104,
102,
94,
93,
92,
91,
88,
85,
80,
79,
74,
73,
70,
64,
63,
62,
61,
60,
48-K,
47-n,
46-K,
45-n,
38,
37,
35,
34,
33-n,
32,
31,
27,
26,
25,
24,
23,
19,
18,
16,
13,
12,
11,
10,
6,
5,
0,
All Forms Known to be False in \(\cal N7\):
430-p,
427,
407,
384,
359,
347,
345,
335-n,
334,
333,
328,
317,
303,
295,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
218,
214,
202,
192,
168,
152,
149,
133,
109,
101,
100,
99,
95-F,
67,
66,
50,
49,
40,
30,
28-p,
20,
15,
14,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 16-23-24-60-91-123-191
Falses that are implied by others list: 30-99-133-152-192-328
References for models trues falses list: References L\"auchli [1964], Jech [1973b](p 104, Thm 7.9), Pincus [1976], Howard/Rubin [1995b],notes 2(8,9), 18, 33, and 120(34 and 47).
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