Fraenkel \(\cal N9\): Halpern/Howard Model | Historical notes
Description: \(A\) is a set of atoms with the structureof the set \( \{s : s:\omega\longrightarrow\omega \wedge (\exists n)(\forall j > n)(s_j = 0)\}\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N9\):
423,
405,
404,
390,
389,
387,
378,
377,
376,
374-n,
373-n,
371,
369,
368,
367,
366,
364,
363,
362,
361,
358,
342-n,
336-n,
325,
313,
309,
307,
306,
305,
304,
296,
289,
288-n,
280,
273,
272,
252,
251,
249,
223,
222,
221,
217,
216,
212,
211,
206,
204,
203,
199(\(n\)),
198,
197,
194,
191,
190,
189,
186,
185,
182,
170,
169,
167,
145,
142,
139,
137-k,
132,
130,
128,
127,
124,
108,
104,
98,
94,
93,
92,
91,
84,
83,
82,
80,
79,
75,
74,
73,
70,
64,
63,
57,
53,
38,
37,
35,
34,
19,
18,
17,
13,
12,
11,
10,
9,
6,
5,
4,
3,
0,
All Forms Known to be False in \(\cal N9\):
409,
408,
407,
399,
391,
384,
345,
344,
343,
335-n,
333,
332,
331,
326,
323,
317,
303,
295,
284,
270,
218,
213,
201,
192,
133,
123,
109,
107,
95-F,
88,
85,
68,
62,
61,
60,
50,
49,
36,
30,
15,
14,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 3-63-91-191
Falses that are implied by others list: 88-133-192
References for models trues falses list: ReferencesHalpern/Howard [1974], notes 18 and 120(56).
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