Fraenkel \(\cal N15\): Brunner/Howard Model I | Historical notes
Description: \(A=\{a_{i,\alpha}: i\in\omega\wedge\alpha\in\omega_1\}\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N15\):
423,
420,
419,
418,
416,
415,
414,
413,
412,
411,
405,
404,
390,
389,
388,
387,
380,
379,
378,
377,
376,
375,
374-n,
373-n,
371,
369,
368,
367,
366,
364,
363,
362,
361,
358,
357,
355,
354,
353,
352,
351,
350,
342-n,
341,
340,
339,
338,
336-n,
327,
325,
313,
309,
307,
306,
305,
304,
296,
289,
288-n,
282,
280,
279,
273,
272,
252,
251,
250,
249,
243,
223,
222,
221,
217,
216,
212,
211,
209,
206,
203,
199(\(n\)),
198,
197,
194,
191,
190,
189,
185,
182,
170,
169,
167,
155,
154,
152,
150,
145,
144,
142,
139,
137-k,
132,
131,
130,
128,
127,
126,
125,
124,
122,
119,
113,
111,
108,
106,
104,
98,
94,
93,
92,
91,
84,
83,
82,
80,
79,
78,
77,
75,
74,
73,
70,
64,
63,
57,
48-K,
47-n,
43,
42,
38,
37,
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 \(\cal N15\):
430-p,
427,
409,
408,
407,
403,
402,
400,
399,
398,
397,
396,
395,
394,
393,
392,
391,
384,
359,
347,
345,
344,
343,
335-n,
334,
333,
332,
331,
330,
329,
328,
324,
323,
322,
317,
303,
302,
295,
292,
286,
270,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
231,
218,
213,
202,
193,
192,
168,
165,
163,
151,
149,
133,
123,
112,
109,
107,
101,
100,
95-F,
85,
68,
67,
66,
62,
60,
50,
49,
40,
36,
30,
28-p,
23,
21,
20,
15,
14,
3,
2,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 43-63-91-122-144-152-191
Falses that are implied by others list: 3-62-151-163-192-193-324-330
References for models trues falses list: References Brunner/Howard [1992], Brunner [1982a], Blass [1979], Howard [1973], notes 18,60, 120(32, 34, 41, and 56), 144, and 155.
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