Fraenkel \(\cal N38\): Howard/Rubin Model I | Historical notes
Description: Let \((A,\le)\) be an ordered set of atomswhich is order isomorphic to \({\Bbb Q}^\omega\), the set of all functionsfrom \(\omega\) into \(\Bbb Q\) ordered by the lexicographic ordering
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N38\):
423,
421,
420,
419,
418,
412,
411,
410,
406,
404,
401,
390,
389,
387,
386,
385,
380,
379,
378,
377,
376,
374-n,
373-n,
371,
370,
369,
368,
367,
366,
364,
363,
362,
361,
358,
357,
356,
355,
354,
353,
352,
351,
350,
349,
344,
343,
342-n,
341,
340,
338,
336-n,
332,
331,
330,
329,
327,
326,
325,
324,
323,
317,
315,
314,
313,
311,
309,
308-p,
307,
306,
305,
304,
298,
296,
295,
294,
293,
289,
288-n,
287,
285,
283,
282,
280,
276,
273,
272,
271-n,
270,
269,
268,
252,
251,
250,
249,
242,
241,
235,
233,
231,
229,
228,
227,
226,
225,
223,
222,
221,
217,
216,
213,
212,
211,
209,
207-alpha,
206,
203,
201,
199(\(n\)),
198,
197,
194,
191,
190,
189,
185,
182,
178-n-N,
170,
169,
167,
165,
154,
153,
151,
150,
146,
145,
142,
141,
140,
139,
137-k,
132,
131,
130,
128,
127,
126,
124,
123,
122,
121,
120-K,
119,
113,
111,
108,
107,
104,
102,
99,
98,
96,
94,
93,
92,
91,
88,
85,
84,
83,
82,
80,
79,
74,
73,
72,
70,
69,
64,
63,
62,
61,
60,
57,
52,
49,
48-K,
47-n,
46-K,
45-n,
38,
37,
35,
34,
33-n,
32,
31,
30,
29,
27,
26,
25,
24,
23,
19,
18,
17,
16,
14,
13,
12,
11,
10,
9,
8,
6,
5,
0,
All Forms Known to be False in \(\cal N38\):
430-p,
427,
407,
391,
388,
359,
347,
345,
335-n,
334,
333,
328,
292,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
253,
239,
218,
214,
202,
193,
192,
188,
181,
179-epsilon,
174-alpha,
168,
163,
152,
149,
144,
133,
118,
115,
114,
112,
109,
106,
101,
100,
95-F,
90,
89,
87-alpha,
67,
66,
51,
44,
43,
40,
28-p,
20,
15,
3,
2,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 23-60-91-113-191-295-317
Falses that are implied by others list: 3-15-51-106-118-144-152-163-181-253-328
References for models trues falses list: References Howard/Rubin [1996],Kelley [1955], Krom [1986], Blass [1979],Brunner [1982a], \cite{1984b}, Howard [1973],Morris [1969], Pincus [1997], notes 2(3), 18, 60, 95,104, 120(28, 34, 45, and 47) and 121.
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