Fraenkel \(\cal N3\): Mostowski's Linearly Ordered Model | Historical notes
Description: \(A\) is countably infinite;\(\precsim\) is a dense linear ordering on \(A\) without first or lastelements (\((A,\precsim) \cong (\Bbb Q,\le)\)); \(\cal G\) is the group of allorder automorphisms on \((A,\precsim)\); and \(S\) is the set of all finitesubsets of \(A\)
Parameter(s): This model does not depend on parameters
All Forms Known to be True in \(\cal N3\):
423,
421,
420,
419,
418,
412,
411,
410,
406,
401,
390,
389,
387,
386,
385,
382,
381,
380,
379,
378,
377,
374-n,
373-n,
371,
370,
369,
368,
367,
366,
364,
363,
362,
361,
358,
357,
356,
352,
350,
349,
344,
343,
342-n,
338,
336-n,
332,
331,
330,
329,
327,
326,
325,
324,
323,
317,
315,
314,
313,
311,
309,
308-p,
307,
306,
305,
298,
294,
293,
289,
288-n,
287,
285,
283,
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,
216,
213,
212,
211,
209,
207-alpha,
206,
203,
201,
199(\(n\)),
198,
197,
194,
191,
190,
189,
182,
178-n-N,
170,
169,
167,
165,
164,
154,
153,
151,
150,
146,
145,
142,
141,
140,
139,
137-k,
132,
130,
128,
127,
124,
123,
122,
121,
120-K,
119,
111,
108,
107,
104,
102,
99,
96,
94,
93,
92,
91,
88,
85,
83,
80,
79,
74,
73,
72,
70,
69,
64,
63,
62,
61,
60,
52,
49,
48-K,
47-n,
46-K,
45-n,
38,
37,
35,
34,
33-n,
32,
31,
30,
27,
26,
25,
24,
23,
19,
18,
17,
16,
14,
13,
12,
11,
10,
6,
5,
0,
All Forms Known to be False in \(\cal N3\):
430-p,
427,
426,
407,
398,
391,
388,
376,
375,
359,
355,
347,
346,
345,
335-n,
334,
333,
328,
322,
316,
304,
296,
295,
292,
290,
286,
264,
262,
261,
260,
259,
258,
257,
256,
255,
253,
239,
218,
214,
202,
200,
193,
192,
188,
185,
181,
179-epsilon,
174-alpha,
168,
161,
157,
156,
155,
152,
149,
147,
144,
133,
131,
129,
126,
125,
118,
115,
114,
113,
112,
109,
106,
101,
100,
97,
95-F,
90,
89,
87-alpha,
86-alpha,
84,
82,
78,
77,
76,
71-alpha,
67,
66,
51,
44,
43,
41,
40,
39,
28-p,
20,
15,
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: 16-23-24-60-128-164-191-317-325-379-381
Falses that are implied by others list: 84-97-118-125-131-147-155-156-157-200-253-290-295-296-304-355-376
References for models trues falses list: References Mostowski [1939] Blass [1977a], Brunner [1982a],\cite{1983a}, \cite{1983c}, \cite{1983d}, \cite{1984c}, \cite{1984f},\cite{1985c}, Dawson/Howard [1976], De la Cruz/Di Prisco [1998b], Gonzalez [1995a], Halpern [1964],Howard [1973], Howard/Keremedis/Rubin\slash Rubin [1998b], Howard/Yorke [1989], Jech [1973b],Krom [1986], L\"auchli [1964], Levy [1958],Pincus [1969], \cite{1997}, Sageev [1981], notes2(8,9), 18 and 120(34 and 45).
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