178:
22:
80:
53:
90:
274:
Technically there is a restriction on the size of the set of individual constants for the theorem to hold, viz. by
Lowenheim-Skolem theorem, at least aleph-null. As per your particular example, the article is misleading, since the theorem pertains, not to satisfiability I think, but validity.
210:
I'm interested to read about the theorem of Beth alluded to in the article. It certainly isn't true that in ordinary first-order logic, anonymous elements of the domain can be ignored; for example the real numbers satisfy
293:
Yes, the article is misleading. I'd like to fix it, but I don't know what it's trying to say. I'm just going to remove that sentence for now, we can always add it later if we figure out how to correct it. — Carl
319:
In the fourth paragraph: "Truth-value semantics is not without its problems. First, the strong completeness theorem and compactness fail" -- can someone give us a pointer as to what the
254:
256:
in the language of rings, but there is no constant symbol for either root. So I am curious what context Beth was working in that made it possible to avoid this issue. — Carl
111:
on
Knowledge. If you would like to support the project, please visit the project page, where you can get more details on how you can help, and where you can join the
374:
148:
138:
369:
384:
113:
379:
347:
389:
324:
103:
58:
332:
33:
185:
63:
328:
21:
351:
39:
214:
280:
95:
276:
177:
363:
301:
263:
355:
336:
306:
284:
268:
108:
85:
297:
259:
107:, a collaborative effort to improve the coverage of content related to
79:
52:
15:
323:
completeness theorem is? It doesn't seem to be mentioned in
176:
346:
The article mentions Dunn and Belnap 1968, which is what?
217:
159:
248:
8:
19:
156:
47:
231:
216:
49:
117:about philosophy content on Knowledge.
7:
101:This article is within the scope of
38:It is of interest to the following
375:Low-importance Philosophy articles
249:{\displaystyle \exists x(x^{2}=2)}
218:
14:
123:Knowledge:WikiProject Philosophy
88:
78:
51:
20:
370:Start-Class Philosophy articles
143:This article has been rated as
126:Template:WikiProject Philosophy
243:
224:
1:
385:Low-importance logic articles
315:"Strong" Completeness Theorem
327:(that I could find). Thanks
325:Gödel's_completeness_theorem
356:23:22, 9 January 2014 (UTC)
337:15:44, 5 October 2010 (UTC)
406:
380:Start-Class logic articles
149:project's importance scale
390:Logic task force articles
184:
155:
142:
73:
46:
307:21:17, 4 May 2008 (UTC)
285:21:16, 4 May 2008 (UTC)
269:13:15, 3 May 2008 (UTC)
160:Associated task forces:
250:
181:
104:WikiProject Philosophy
28:This article is rated
251:
180:
215:
329:BrideOfKripkenstein
129:Philosophy articles
246:
182:
114:general discussion
34:content assessment
305:
267:
203:
202:
199:
198:
195:
194:
191:
190:
96:Philosophy portal
397:
342:Reference needed
295:
257:
255:
253:
252:
247:
236:
235:
167:
157:
131:
130:
127:
124:
121:
98:
93:
92:
91:
82:
75:
74:
69:
66:
55:
48:
31:
25:
24:
16:
405:
404:
400:
399:
398:
396:
395:
394:
360:
359:
344:
317:
227:
213:
212:
208:
206:Theorem of Beth
165:
128:
125:
122:
119:
118:
94:
89:
87:
67:
61:
32:on Knowledge's
29:
12:
11:
5:
403:
401:
393:
392:
387:
382:
377:
372:
362:
361:
343:
340:
316:
313:
312:
311:
310:
309:
288:
287:
245:
242:
239:
234:
230:
226:
223:
220:
207:
204:
201:
200:
197:
196:
193:
192:
189:
188:
183:
173:
172:
170:
168:
162:
161:
153:
152:
145:Low-importance
141:
135:
134:
132:
100:
99:
83:
71:
70:
68:Low‑importance
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
402:
391:
388:
386:
383:
381:
378:
376:
373:
371:
368:
367:
365:
358:
357:
353:
349:
348:86.185.216.86
341:
339:
338:
334:
330:
326:
322:
314:
308:
303:
299:
292:
291:
290:
289:
286:
282:
278:
273:
272:
271:
270:
265:
261:
240:
237:
232:
228:
221:
205:
187:
179:
175:
174:
171:
169:
164:
163:
158:
154:
150:
146:
140:
137:
136:
133:
116:
115:
110:
106:
105:
97:
86:
84:
81:
77:
76:
72:
65:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
345:
320:
318:
209:
144:
112:
102:
40:WikiProjects
30:Start-class
364:Categories
120:Philosophy
109:philosophy
59:Philosophy
277:Nortexoid
147:on the
321:strong
36:scale.
186:Logic
64:Logic
352:talk
333:talk
302:talk
281:talk
264:talk
298:CBM
260:CBM
139:Low
366::
354:)
335:)
300:·
283:)
262:·
219:∃
166:/
62::
350:(
331:(
304:)
296:(
279:(
266:)
258:(
244:)
241:2
238:=
233:2
229:x
225:(
222:x
151:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
