211:
85:. There are several different options for the topology of κ. The simplest option is to take the usual product topology. Another option is to take the topology generated by open sets consisting of functions whose value is specified on less than λ elements of λ.
58:
with at least λ elements but generated by a countable number of elements. As the size of countably generated complete
Boolean algebras is unbounded, this shows that there is no
252:
160:
126:
276:
17:
32:
245:
121:. Oxford Logic Guides. Vol. 12 (2nd ed.). Oxford: Oxford University Press (Clarendon Press).
271:
55:
281:
238:
36:
226:
178:
136:
8:
115:
166:
156:
122:
82:
174:
132:
74:
152:
40:
222:
186:
48:
265:
170:
78:
59:
144:
210:
189:(1963). "Independence results in set theory by Cohen's method. IV".
70:
There are several slightly different sorts of collapsing algebras.
218:
44:
62:
complete
Boolean algebra on a countable number of elements.
117:
81:κ is a collapsing algebra. Here κ and λ are both given the
47:
used to generate collapsing algebras were introduced by
73:
If κ and λ are cardinals, then the
Boolean algebra of
151:(third millennium (revised and expanded) ed.).
114:
95:
263:
246:
253:
239:
14:
264:
205:
185:
143:
112:
101:
39:to reduce ("collapse") the size of
24:
25:
293:
54:The collapsing algebra of λ is a
209:
13:
1:
88:
65:
225:. You can help Knowledge by
7:
10:
298:
204:
56:complete Boolean algebra
191:Notices Amer. Math. Soc
221:-related article is a
277:Forcing (mathematics)
113:Bell, J. L. (1985).
35:sometimes used in
29:collapsing algebra
27:In mathematics, a
234:
233:
83:discrete topology
75:regular open sets
16:(Redirected from
289:
255:
248:
241:
213:
206:
198:
182:
140:
120:
105:
99:
21:
297:
296:
292:
291:
290:
288:
287:
286:
272:Boolean algebra
262:
261:
260:
259:
202:
163:
153:Springer-Verlag
129:
109:
108:
100:
96:
91:
68:
33:Boolean algebra
23:
22:
15:
12:
11:
5:
295:
285:
284:
279:
274:
258:
257:
250:
243:
235:
232:
231:
214:
200:
199:
183:
161:
141:
127:
107:
106:
104:, p. 593.
93:
92:
90:
87:
67:
64:
9:
6:
4:
3:
2:
294:
283:
282:Algebra stubs
280:
278:
275:
273:
270:
269:
267:
256:
251:
249:
244:
242:
237:
236:
230:
228:
224:
220:
215:
212:
208:
207:
203:
196:
192:
188:
184:
180:
176:
172:
168:
164:
162:3-540-44085-2
158:
154:
150:
146:
142:
138:
134:
130:
128:0-19-853241-5
124:
119:
118:
111:
110:
103:
98:
94:
86:
84:
80:
79:product space
76:
71:
63:
61:
57:
52:
50:
46:
42:
38:
34:
31:is a type of
30:
19:
18:Levy collapse
227:expanding it
216:
201:
194:
190:
187:Lévy, Azriel
148:
145:Jech, Thomas
116:
97:
72:
69:
53:
28:
26:
49:Azriel Lévy
266:Categories
179:1007.03002
149:Set theory
137:0585.03021
89:References
66:Definition
171:174929965
102:Lévy 1963
51:in 1963.
41:cardinals
147:(2003).
219:algebra
77:of the
37:forcing
177:
169:
159:
135:
125:
45:posets
43:. The
217:This
223:stub
167:OCLC
157:ISBN
123:ISBN
60:free
175:Zbl
133:Zbl
268::
195:10
193:.
173:.
165:.
155:.
131:.
254:e
247:t
240:v
229:.
197:.
181:.
139:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.