Fraenkel \(\cal N53\): Good/Tree/Watson Model I | Historical notes
Description: Let \(A=\bigcup \{Q_n:\ n\in\omega\}\), where \(Q_n=\{a_{n,q}:q\in \Bbb{Q}\}\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N53\):
423,
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,
203,
199(\(n\)),
198,
197,
194,
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,
74,
73,
70,
64,
63,
57,
38,
37,
35,
34,
19,
18,
17,
13,
12,
11,
10,
9,
6,
5,
0,
All Forms Known to be False in \(\cal N53\):
430-p,
427,
409,
408,
407,
399,
394,
392,
391,
384,
382,
381,
359,
347,
345,
344,
343,
337,
335-n,
334,
333,
332,
331,
326,
323,
317,
303,
302,
295,
292,
286,
284,
270,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
232,
218,
213,
202,
201,
192,
168,
149,
133,
123,
114,
112,
109,
107,
101,
100,
95-F,
90,
89,
88,
85,
68,
67,
66,
62,
61,
60,
51,
50,
49,
40,
36,
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: 9-63-91
Falses that are implied by others list: 88-192-232-337-382
References for models trues falses list: ReferencesGood/Tree/Watson [1996], Howard\slash Keremedis\slashRubin\slash Rubin [1998b], \ac{Howard\slash Keremedis\slashRubin\slash Stanley\slash Tachtsis}\newline \cite{1999}, notes 18 and 120(4, 20, and 56).
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