45:. In the universe view the continuum hypothesis is a meaningful question that is either true or false though we have not yet been able to decide which. In the multiverse view it is meaningless to ask whether the continuum hypothesis is true or false before selecting a model of set theory. Another difference is that the statement "For every transitive model of ZFC there is a larger model of ZFC in which it is countable" is true in some versions of the multiverse view of mathematics but is false in the universe view.
138:
26:
view is that there are many models of set theory, but no "absolute", "canonical" or "true" model. The various models are all equally valid or true, though some may be more useful or attractive than others. The opposite view is the "universe" view of set theory in which all sets are contained in some
179:
208:
203:
213:
31:
172:
55:
Antos, Carolin; Friedman, Sy-David; Honzik, Radek; Ternullo, Claudio (2015), "Multiverse conceptions in set theory",
165:
105:
42:
198:
145:
95:
83:
113:
64:
125:
76:
121:
72:
109:
149:
41:
A typical difference between the universe and multiverse views is the attitude to the
192:
117:
68:
22:
17:
137:
100:
153:
30:The collection of countable transitive models of
173:
8:
180:
166:
38:and is very similar to the "multiverse".
99:
86:(2012), "The set-theoretic multiverse",
7:
134:
132:
14:
34:(in some universe) is called the
136:
1:
152:. You can help Knowledge by
230:
209:Foundations of mathematics
131:
204:Philosophy of mathematics
118:10.1017/S1755020311000359
69:10.1007/s11229-015-0819-9
214:Mathematical logic stubs
27:single ultimate model.
148:-related article is a
43:continuum hypothesis
110:2011arXiv1108.4223H
146:mathematical logic
161:
160:
221:
182:
175:
168:
140:
133:
128:
103:
79:
63:(8): 2463–2488,
16:In mathematical
229:
228:
224:
223:
222:
220:
219:
218:
189:
188:
187:
186:
88:Rev. Symb. Log.
82:
54:
51:
12:
11:
5:
227:
225:
217:
216:
211:
206:
201:
191:
190:
185:
184:
177:
170:
162:
159:
158:
141:
130:
129:
94:(3): 416–449,
84:Hamkins, J. D.
80:
50:
47:
13:
10:
9:
6:
4:
3:
2:
226:
215:
212:
210:
207:
205:
202:
200:
197:
196:
194:
183:
178:
176:
171:
169:
164:
163:
157:
155:
151:
147:
142:
139:
135:
127:
123:
119:
115:
111:
107:
102:
97:
93:
89:
85:
81:
78:
74:
70:
66:
62:
58:
53:
52:
48:
46:
44:
39:
37:
33:
28:
25:
24:
19:
154:expanding it
143:
91:
87:
60:
56:
40:
35:
29:
21:
15:
199:Set theory
193:Categories
49:References
36:hyperverse
23:multiverse
18:set theory
101:1108.4223
57:Synthese
126:2970696
106:Bibcode
77:3400617
124:
75:
20:, the
144:This
96:arXiv
150:stub
114:doi
65:doi
61:192
32:ZFC
195::
122:MR
120:,
112:,
104:,
90:,
73:MR
71:,
59:,
181:e
174:t
167:v
156:.
116::
108::
98::
92:5
67::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
