Knowledge (XXG)

Jónsson–Tarski algebra

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then it can be extended to a unique Jónsson–Tarski algebra by letting
446:
Smirnov, D. M. (1971), "Cantor algebras with one generator. I.",
335:. The definition for type > 2 is similar but with 78: 8: 177:A Jónsson–Tarski algebra of type 2 is a set 97:and Cantor's theorem that an infinite set 414:Jónsson, Bjarni; Tarski, Alfred (1961), 86: 117:is also occasionally used to mean the 7: 416:"On two properties of free algebras" 103:has the same number of elements as 14: 156:Jónsson–Tarski algebra on one 150:order-preserving automorphisms 1: 129:, or the Boolean algebra of 510: 205:and two 'projection' maps 69:. They were introduced by 15: 22:Lindenbaum–Tarski algebra 16:Not to be confused with 355:is any bijection from 341:projection operators. 141:(sometimes called the 33:Jónsson–Tarski algebra 387:be the projection of 81:, Theorem 5). 494:Algebraic structures 93:because of Cantor's 89:), named them after 41:algebraic structure 462:10.1007/BF02217801 71:Bjarni Jónsson 449:Algebra and Logic 501: 480: 442: 403: 397: 386: 370: 364: 354: 340: 334: 302: 268: 234: 228: 222: 213: 204: 198: 188: 182: 168: 112: 102: 95:pairing function 68: 55: 509: 508: 504: 503: 502: 500: 499: 498: 484: 483: 445: 413: 410: 399: 388: 380: 372: 366: 356: 350: 347: 336: 325: 314: 304: 301: 294: 287: 276: 270: 267: 260: 253: 242: 236: 230: 224: 221: 215: 212: 206: 200: 190: 184: 183:with a product 178: 175: 164: 119:Boolean algebra 104: 98: 60: 51: 25: 18:Jónsson algebra 12: 11: 5: 507: 505: 497: 496: 486: 485: 482: 481: 443: 409: 406: 376: 346: 343: 323: 312: 299: 292: 285: 274: 265: 258: 251: 240: 219: 210: 174: 171: 162:Thompson group 123:clopen subsets 115:Cantor algebra 37:Cantor algebra 13: 10: 9: 6: 4: 3: 2: 506: 495: 492: 491: 489: 479: 475: 471: 467: 463: 459: 455: 451: 450: 444: 441: 437: 433: 429: 425: 421: 417: 412: 411: 407: 405: 402: 395: 391: 384: 379: 375: 369: 363: 359: 353: 344: 342: 339: 333: 329: 322: 318: 311: 307: 298: 291: 284: 280: 273: 264: 257: 250: 246: 239: 235:, satisfying 233: 227: 218: 209: 203: 197: 193: 187: 181: 172: 170: 167: 163: 159: 155: 151: 148:The group of 146: 144: 143:Cohen algebra 140: 136: 132: 131:Borel subsets 128: 124: 120: 116: 111: 107: 101: 96: 92: 88: 84: 80: 76: 75:Alfred Tarski 73: and 72: 67: 63: 59: 54: 50: 46: 42: 38: 34: 30: 23: 19: 453: 447: 423: 420:Math. Scand. 419: 400: 393: 389: 382: 377: 373: 367: 361: 357: 351: 348: 337: 331: 327: 320: 316: 309: 305: 296: 289: 282: 278: 271: 262: 255: 248: 244: 237: 231: 225: 216: 207: 201: 195: 191: 185: 179: 176: 165: 147: 114: 109: 105: 99: 91:Georg Cantor 65: 61: 52: 49:infinite set 36: 32: 26: 404:th factor. 139:meager sets 113:. The term 43:encoding a 29:mathematics 478:0223.08006 440:0111.02002 426:: 95–101, 408:References 173:Definition 127:Cantor set 456:: 40–49, 398:onto the 158:generator 56:onto the 45:bijection 488:Category 47:from an 470:0296006 432:0126399 345:Example 160:is the 152:of the 137:modulo 133:of the 125:of the 121:of all 85: ( 83:Smirnov 77: ( 58:product 476:  468:  438:  430:  303:, and 39:is an 330:)) = 295:)) = 261:)) = 223:from 189:from 135:reals 214:and 154:free 87:1971 79:1961 31:, a 474:Zbl 458:doi 436:Zbl 365:to 349:If 229:to 199:to 145:). 35:or 27:In 20:or 490:: 472:, 466:MR 464:, 454:10 452:, 434:, 428:MR 422:, 418:, 319:), 269:, 169:. 460:: 424:9 401:i 396:) 394:a 392:( 390:w 385:) 383:a 381:( 378:i 374:p 368:A 362:A 360:× 358:A 352:w 338:n 332:a 328:a 326:( 324:2 321:p 317:a 315:( 313:1 310:p 308:( 306:w 300:2 297:a 293:2 290:a 288:, 286:1 283:a 281:( 279:w 277:( 275:2 272:p 266:1 263:a 259:2 256:a 254:, 252:1 249:a 247:( 245:w 243:( 241:1 238:p 232:A 226:A 220:2 217:p 211:1 208:p 202:A 196:A 194:× 192:A 186:w 180:A 166:F 110:X 108:× 106:X 100:X 66:X 64:× 62:X 53:X 24:.

Index

Jónsson algebra
Lindenbaum–Tarski algebra
mathematics
algebraic structure
bijection
infinite set
product
Bjarni Jónsson
Alfred Tarski
1961
Smirnov
1971
Georg Cantor
pairing function
Boolean algebra
clopen subsets
Cantor set
Borel subsets
reals
meager sets
Cohen algebra
order-preserving automorphisms
free
generator
Thompson group
"On two properties of free algebras"
MR
0126399
Zbl
0111.02002

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