Fraenkel \(\cal N39\): Howard's Model II | Historical notes
Description: \(A\) is denumerable and is a disjoint union\(\bigcup_{i\in\omega}B_i\cup\bigcup_{i\in\omega}C_i\), where for all\(i\in\omega, |B_i|=|C_i|=\aleph_0\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N39\):
423,
421,
420,
419,
389,
374-n,
373-n,
371,
369,
368,
367,
366,
364,
363,
362,
361,
358,
357,
352,
350,
338,
330,
327,
324,
315,
313,
309,
307,
306,
305,
294,
289,
288-n,
280,
273,
272,
252,
251,
250,
249,
231,
223,
222,
216,
212,
211,
209,
207-alpha,
206,
203,
199(\(n\)),
197,
194,
191,
190,
189,
182,
170,
169,
165,
151,
145,
142,
139,
137-k,
130,
122,
119,
111,
108,
104,
94,
93,
92,
91,
80,
79,
74,
70,
48-K,
47-n,
38,
37,
35,
34,
32,
31,
27,
26,
25,
24,
23,
19,
18,
16,
13,
10,
6,
5,
0,
All Forms Known to be False in \(\cal N39\):
430-p,
427,
426,
407,
388,
359,
347,
346,
345,
335-n,
334,
333,
328,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
218,
214,
202,
193,
192,
188,
181,
174-alpha,
168,
152,
149,
131,
126,
113,
109,
106,
101,
100,
95-F,
87-alpha,
86-alpha,
76,
67,
66,
44,
43,
40,
39,
29,
28-p,
21,
20,
15,
8,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 16-23-24-91-191-231
Falses that are implied by others list: 15-29-131-152
References for models trues falses list: References Howard [1994], notes 2(8, 9), 18 and 120(33, 47, and49).
Back