Knowledge

Axiom of real determinacy

Source 📝

25: 300: 42: 341: 89: 61: 108: 68: 231: 46: 75: 360: 334: 57: 370: 327: 214: 35: 82: 365: 179: 159: 279: 269: 236: 195: 311: 203: 163: 354: 199: 191: 171: 167: 155: 122: 24: 307: 274: 141: 283: 257: 182:(AD), which makes the same statement about games where both players choose 299: 183: 137: 256:
Ikegami, Daisuke; de Kloet, David; Löwe, Benedikt (2012-11-01).
226: 18: 178:
The axiom of real determinacy is a stronger version of the
315: 49:. Unsourced material may be challenged and removed. 170:is determined, i.e., one of the two players has a 335: 8: 148: 342: 328: 273: 258:"The axiom of real Blackwell determinacy" 109:Learn how and when to remove this message 248: 7: 296: 294: 47:adding citations to reliable sources 198:. It also implies the existence of 14: 298: 23: 232:Axiom of projective determinacy 34:needs additional citations for 262:Archive for Mathematical Logic 1: 213:is equivalent to AD plus the 162:. Then, every game of length 154:Consider infinite two-person 314:. You can help Knowledge by 144:. It states the following: 58:"Axiom of real determinacy" 387: 293: 166:where both players choose 275:10.1007/s00153-012-0291-x 127:axiom of real determinacy 215:axiom of uniformization 310:-related article is a 361:Axioms of set theory 180:axiom of determinacy 43:improve this article 160:perfect information 152: —  16:Axiom of set theory 150: 323: 322: 119: 118: 111: 93: 378: 371:Set theory stubs 344: 337: 330: 302: 295: 288: 287: 277: 253: 237:Topological game 172:winning strategy 153: 129:(abbreviated as 114: 107: 103: 100: 94: 92: 51: 27: 19: 386: 385: 381: 380: 379: 377: 376: 375: 351: 350: 349: 348: 292: 291: 255: 254: 250: 245: 223: 212: 204:large cardinals 196:axiom of choice 189: 176: 151: 134: 115: 104: 98: 95: 52: 50: 40: 28: 17: 12: 11: 5: 384: 382: 374: 373: 368: 363: 353: 352: 347: 346: 339: 332: 324: 321: 320: 303: 290: 289: 268:(7): 671–685. 247: 246: 244: 241: 240: 239: 234: 229: 222: 219: 210: 187: 146: 132: 117: 116: 31: 29: 22: 15: 13: 10: 9: 6: 4: 3: 2: 383: 372: 369: 367: 364: 362: 359: 358: 356: 345: 340: 338: 333: 331: 326: 325: 319: 317: 313: 309: 304: 301: 297: 285: 281: 276: 271: 267: 263: 259: 252: 249: 242: 238: 235: 233: 230: 228: 225: 224: 220: 218: 216: 207: 205: 202:with certain 201: 197: 193: 185: 181: 175: 173: 169: 165: 161: 157: 145: 143: 139: 135: 128: 124: 113: 110: 102: 91: 88: 84: 81: 77: 74: 70: 67: 63: 60: –  59: 55: 54:Find sources: 48: 44: 38: 37: 32:This article 30: 26: 21: 20: 316:expanding it 305: 265: 261: 251: 208: 200:inner models 192:inconsistent 177: 168:real numbers 147: 130: 126: 120: 105: 96: 86: 79: 72: 65: 53: 41:Please help 36:verification 33: 366:Determinacy 123:mathematics 355:Categories 308:set theory 243:References 142:set theory 99:March 2024 69:newspapers 284:1432-0665 194:with the 221:See also 184:integers 136:) is an 83:scholar 282:  125:, the 85:  78:  71:  64:  56:  306:This 158:with 156:games 149:Axiom 138:axiom 90:JSTOR 76:books 312:stub 280:ISSN 186:; AD 62:news 270:doi 190:is 140:in 121:In 45:by 357:: 278:. 266:51 264:. 260:. 227:AD 217:. 209:AD 206:. 174:. 131:AD 343:e 336:t 329:v 318:. 286:. 272:: 211:R 188:R 164:ω 133:R 112:) 106:( 101:) 97:( 87:· 80:· 73:· 66:· 39:.

Index


verification
improve this article
adding citations to reliable sources
"Axiom of real determinacy"
news
newspapers
books
scholar
JSTOR
Learn how and when to remove this message
mathematics
axiom
set theory
games
perfect information
ω
real numbers
winning strategy
axiom of determinacy
integers
inconsistent
axiom of choice
inner models
large cardinals
axiom of uniformization
AD
Axiom of projective determinacy
Topological game
"The axiom of real Blackwell determinacy"

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.