Fraenkel \(\cal N1\): The Basic Fraenkel Model | Historical notes
Description: The set of atoms, \(A\) is denumerable; \(\cal G\) is the group of all permutations on \(A\); and \(S\) isthe set of all finite subsets of \(A\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N1\):
423,
421,
420,
419,
397,
396,
395,
389,
380,
379,
374-n,
373-n,
371,
369,
368,
367,
366,
364,
363,
362,
361,
358,
357,
355,
352,
350,
342-n,
341,
340,
338,
337,
330,
327,
325,
324,
322,
316,
315,
313,
309,
307,
306,
305,
304,
294,
289,
288-n,
280,
273,
272,
263,
254,
252,
251,
250,
249,
242,
241,
233,
232,
231,
223,
222,
221,
217,
216,
212,
211,
209,
208,
207-alpha,
206,
203,
199(\(n\)),
197,
194,
191,
190,
189,
185,
182,
173,
170,
169,
167,
165,
151,
147,
145,
142,
139,
137-k,
135,
134,
133,
132,
130,
127,
124,
122,
119,
118,
116,
115,
114,
112,
111,
108,
104,
94,
93,
92,
91,
90,
89,
84,
80,
79,
77,
74,
73,
70,
63,
58,
51,
48-K,
47-n,
38,
37,
35,
34,
32,
31,
27,
26,
25,
24,
23,
19,
18,
17,
16,
13,
10,
6,
5,
0,
All Forms Known to be False in \(\cal N1\):
430-p,
427,
426,
409,
408,
407,
405,
404,
399,
391,
390,
388,
387,
384,
378,
377,
376,
359,
347,
346,
345,
344,
343,
336-n,
335-n,
334,
333,
332,
331,
328,
326,
323,
317,
303,
296,
295,
292,
286,
284,
278,
270,
267,
264,
262,
261,
260,
259,
258,
257,
256,
255,
239,
218,
215,
214,
213,
202,
201,
200,
193,
192,
188,
181,
177,
174-alpha,
168,
161,
152,
149,
146,
131,
129,
128,
126,
123,
113,
109,
107,
106,
101,
100,
95-F,
88,
87-alpha,
86-alpha,
85,
83,
82,
76,
75,
71-alpha,
69,
68,
67,
66,
64,
62,
61,
60,
57,
53,
50,
49,
45-n,
44,
43,
41,
40,
39,
36,
30,
28-p,
20,
15,
14,
12,
11,
9,
8,
7,
4,
3,
2,
1,
A minimial list of forms whose truth in this model imply all others that are true in this model: 16-23-24-89-112-114-115-116-127-133-134-135-147-191-217-232-233-263-304-322-325-379-380
Falses that are implied by others list: 53-69-128-131-146-177-200-267-278-292-390
References for models trues falses list: References include Blass [1977a],Brunner [1981a], \cite{1982a}, \cite{1983d}, \cite{1984b},\cite{1984f}, \cite{1985a}, Dawson/Howard [1976], De laCruz/Di Prisco [1998a], Fraenkel [1922], Felgner/Jech [1973], Felgner [1971a], Jech [1973b],Jech/Sochor [1966a], Halpern [1964], Harper/Rubin [1976], Hickman [1976], Hodges [1974],Howard/Keremedis/Rubin/Stanley [1999], Howard/Rubin [1977], L\"auchli [1962], Levy [1958],Pincus [1969], Specker [1957], Stavi [1975],notes 2(8,9), 18, 41, 46, 52, 64, 66, 88, 89, 105, 109, 116, 120(56) and123.
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