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Collapsing algebra

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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.
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complete Boolean algebra on a countable number of elements.
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Boolean-Valued Models and Independence Proofs in Set Theory
81:κ is a collapsing algebra. Here κ and λ are both given the 47:
used to generate collapsing algebras were introduced by
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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:)

Index

Levy collapse
Boolean algebra
forcing
cardinals
posets
Azriel Lévy
complete Boolean algebra
free
regular open sets
product space
discrete topology
Lévy 1963
Boolean-Valued Models and Independence Proofs in Set Theory
ISBN
0-19-853241-5
Zbl
0585.03021
Jech, Thomas
Springer-Verlag
ISBN
3-540-44085-2
OCLC
174929965
Zbl
1007.03002
Lévy, Azriel
Stub icon
algebra
stub
expanding it

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