274:
88:
More generally, for any infinite cardinal κ, a κ-Suslin tree is a tree of height κ such that every branch and antichain has cardinality less than κ. In particular a Suslin tree is the same as a ω
315:
136:
215:
131:
166:
54:
105:
339:
308:
334:
40:
344:
25:
301:
121:
141:
101:
211:
162:
78:
70:
21:
285:
253:
245:
221:
181:
195:
257:
249:
225:
191:
66:
47:
328:
233:
203:
186:
36:
154:
126:
58:
172:
Jensen, R. Björn (1972), "The fine structure of the constructible hierarchy.",
281:
32:
161:, 3rd millennium ed., 2003, Springer Monographs in Mathematics, Springer,
273:
210:, Studies in Logic, vol. 34, London: College Publications,
97:
74:
289:
100:then there is a κ-Suslin tree for every infinite
57:of ZFC, and is equivalent to the existence of a
112:-Suslin tree, is a longstanding open problem.
309:
8:
77:, implies that there is a Suslin tree, and
316:
302:
85:) implies that there are no Suslin trees.
185:
137:List of unsolved problems in set theory
93:
62:
132:List of statements independent of ZFC
7:
270:
268:
288:. You can help Knowledge (XXG) by
53:The existence of a Suslin tree is
14:
31:such that every branch and every
272:
234:"Ensembles ordonnés et ramifiés"
106:Generalized Continuum Hypothesis
1:
199:erratum, ibid. 4 (1972), 443.
108:implies the existence of an ℵ
187:10.1016/0003-4843(72)90001-0
361:
267:
238:Publ. Math. Univ. Belgrade
41:Mikhail Yakovlevich Suslin
46:Every Suslin tree is an
39:. They are named after
284:-related article is a
122:Glossary of set theory
340:Independence results
232:Kurepa, G. (1935),
73:, a consequence of
335:Trees (set theory)
102:successor cardinal
16:In mathematics, a
297:
296:
217:978-1-84890-050-9
71:diamond principle
352:
345:Set theory stubs
318:
311:
304:
276:
269:
260:
228:
198:
189:
174:Ann. Math. Logic
142:Suslin's problem
360:
359:
355:
354:
353:
351:
350:
349:
325:
324:
323:
322:
265:
263:
231:
218:
202:
171:
150:
118:
111:
104:κ. Whether the
96:showed that if
92:-Suslin tree.
91:
84:
29:
12:
11:
5:
358:
356:
348:
347:
342:
337:
327:
326:
321:
320:
313:
306:
298:
295:
294:
277:
262:
261:
229:
216:
204:Kunen, Kenneth
200:
180:(3): 229–308,
169:
151:
149:
146:
145:
144:
139:
134:
129:
124:
117:
114:
109:
89:
82:
79:Martin's axiom
67:Suslin algebra
48:Aronszajn tree
27:
13:
10:
9:
6:
4:
3:
2:
357:
346:
343:
341:
338:
336:
333:
332:
330:
319:
314:
312:
307:
305:
300:
299:
293:
291:
287:
283:
278:
275:
271:
266:
259:
255:
251:
247:
243:
239:
235:
230:
227:
223:
219:
213:
209:
205:
201:
197:
193:
188:
183:
179:
175:
170:
168:
167:3-540-44085-2
164:
160:
156:
153:
152:
147:
143:
140:
138:
135:
133:
130:
128:
125:
123:
120:
119:
115:
113:
107:
103:
99:
95:
94:Jensen (1972)
86:
80:
76:
72:
68:
64:
63:Kurepa (1935)
60:
56:
51:
49:
44:
42:
38:
34:
30:
23:
19:
290:expanding it
279:
264:
241:
237:
207:
177:
173:
158:
87:
52:
45:
17:
15:
155:Thomas Jech
127:Kurepa tree
59:Suslin line
55:independent
35:is at most
18:Suslin tree
329:Categories
282:set theory
258:0014.39401
250:61.0980.01
226:1262.03001
208:Set theory
159:Set Theory
148:References
61:(shown by
24:of height
244:: 1–138,
37:countable
33:antichain
206:(2011),
116:See also
196:0309729
65:) or a
256:
248:
224:
214:
194:
165:
69:. The
280:This
20:is a
286:stub
212:ISBN
163:ISBN
81:MA(ℵ
22:tree
254:Zbl
246:JFM
222:Zbl
182:doi
98:V=L
75:V=L
331::
252:,
240:,
236:,
220:,
192:MR
190:,
176:,
157:,
50:.
43:.
317:e
310:t
303:v
292:.
242:4
184::
178:4
110:2
90:1
83:1
28:1
26:ω
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.