Knowledge (XXG)

Computable isomorphism

Source 📝

459: 103: 179: 151: 316: 214: 260: 240: 443: 44: 284: 123: 524: 500: 17: 436: 529: 374: 220: 519: 429: 72: 493: 409: 327: 156: 128: 486: 289: 362: 466: 331: 370: 470: 413: 184: 384: 380: 245: 225: 23: 269: 108: 59: 47: 513: 318:. Computably isomorphic numberings induce the same notion of computability on a set. 330:, the relation of computable isomorphism coincides with the relation of mutual 62: 66: 458: 367:
Theory of recursive functions and effective computability
352:
Theory of recursive functions and effective computability
474: 417: 292: 272: 248: 228: 187: 159: 131: 111: 75: 26: 98:{\displaystyle f\colon \mathbb {N} \to \mathbb {N} } 310: 278: 254: 234: 208: 173: 145: 117: 97: 38: 494: 437: 8: 501: 487: 444: 430: 369:(2nd ed.), Cambridge, MA: MIT Press, 291: 271: 247: 227: 186: 167: 166: 158: 139: 138: 130: 110: 91: 90: 83: 82: 74: 25: 343: 266:if there exists a computable bijection 174:{\displaystyle B\subseteq \mathbb {N} } 146:{\displaystyle A\subseteq \mathbb {N} } 7: 455: 453: 397: 395: 350:Theorem 7.VI, Hartley Rogers, Jr., 525:Theoretical computer science stubs 473:. You can help Knowledge (XXG) by 416:. You can help Knowledge (XXG) by 14: 457: 311:{\displaystyle \nu =\mu \circ f} 197: 191: 87: 1: 410:theoretical computer science 546: 452: 394: 328:Myhill isomorphism theorem 530:Mathematical logic stubs 105:such that the image of 520:Reduction (complexity) 469:-related article is a 412:–related article is a 312: 280: 256: 236: 210: 209:{\displaystyle f(A)=B} 175: 147: 119: 99: 56:recursively isomorphic 40: 313: 281: 264:computably isomorphic 257: 237: 211: 176: 148: 120: 100: 52:computably isomorphic 41: 332:one-one reducibility 290: 270: 255:{\displaystyle \mu } 246: 235:{\displaystyle \nu } 226: 185: 157: 129: 109: 73: 24: 18:computability theory 363:Rogers, Hartley Jr. 39:{\displaystyle A,B} 467:mathematical logic 308: 276: 252: 232: 206: 171: 143: 115: 95: 58:if there exists a 36: 482: 481: 425: 424: 279:{\displaystyle f} 118:{\displaystyle f} 537: 503: 496: 489: 461: 454: 446: 439: 432: 401:P ≟ NP 396: 387: 354: 348: 317: 315: 314: 309: 285: 283: 282: 277: 261: 259: 258: 253: 241: 239: 238: 233: 215: 213: 212: 207: 180: 178: 177: 172: 170: 152: 150: 149: 144: 142: 124: 122: 121: 116: 104: 102: 101: 96: 94: 86: 45: 43: 42: 37: 545: 544: 540: 539: 538: 536: 535: 534: 510: 509: 508: 507: 451: 450: 403: 392: 377: 361: 358: 357: 349: 345: 340: 324: 288: 287: 268: 267: 244: 243: 224: 223: 183: 182: 155: 154: 127: 126: 107: 106: 71: 70: 48:natural numbers 22: 21: 12: 11: 5: 543: 541: 533: 532: 527: 522: 512: 511: 506: 505: 498: 491: 483: 480: 479: 462: 449: 448: 441: 434: 426: 423: 422: 405: 399: 390: 389: 375: 356: 355: 342: 341: 339: 336: 323: 320: 307: 304: 301: 298: 295: 275: 251: 231: 205: 202: 199: 196: 193: 190: 169: 165: 162: 141: 137: 134: 125:restricted to 114: 93: 89: 85: 81: 78: 35: 32: 29: 13: 10: 9: 6: 4: 3: 2: 542: 531: 528: 526: 523: 521: 518: 517: 515: 504: 499: 497: 492: 490: 485: 484: 478: 476: 472: 468: 463: 460: 456: 447: 442: 440: 435: 433: 428: 427: 421: 419: 415: 411: 406: 402: 398: 393: 386: 382: 378: 376:0-262-68052-1 372: 368: 364: 360: 359: 353: 347: 344: 337: 335: 333: 329: 321: 319: 305: 302: 299: 296: 293: 273: 265: 249: 229: 222: 219:Further, two 217: 203: 200: 194: 188: 163: 160: 135: 132: 112: 79: 76: 68: 64: 61: 57: 53: 49: 33: 30: 27: 19: 475:expanding it 464: 418:expanding it 407: 400: 391: 366: 351: 346: 325: 263: 218: 55: 51: 15: 262:are called 514:Categories 338:References 221:numberings 63:computable 303:∘ 300:μ 294:ν 250:μ 230:ν 164:⊆ 136:⊆ 88:→ 80:: 69:function 67:bijective 20:two sets 365:(1987), 322:Theorems 286:so that 385:0886890 326:By the 181:, i.e. 153:equals 404:  383:  373:  465:This 408:This 60:total 471:stub 414:stub 371:ISBN 242:and 65:and 50:are 54:or 46:of 16:In 516:: 381:MR 379:, 334:. 216:. 502:e 495:t 488:v 477:. 445:e 438:t 431:v 420:. 388:. 306:f 297:= 274:f 204:B 201:= 198:) 195:A 192:( 189:f 168:N 161:B 140:N 133:A 113:f 92:N 84:N 77:f 34:B 31:, 28:A

Index

computability theory
natural numbers
total
computable
bijective
numberings
Myhill isomorphism theorem
one-one reducibility
Rogers, Hartley Jr.
ISBN
0-262-68052-1
MR
0886890
theoretical computer science
stub
expanding it
v
t
e
Stub icon
mathematical logic
stub
expanding it
v
t
e
Categories
Reduction (complexity)
Theoretical computer science stubs
Mathematical logic stubs

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