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Barwise compactness theorem

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Computable Structures and the Hyperarithmetic Hierarchy
280: 256: 236: 216: 189: 169: 142: 122: 98: 78: 54: 286: 262: 242: 222: 202: 175: 155: 128: 104: 84: 60: 40:. It was stated and proved by Barwise in 1967. 429: 8: 455:Theorems in the foundations of mathematics 436: 422: 279: 255: 235: 215: 194: 188: 168: 147: 141: 121: 97: 77: 53: 7: 390: 388: 306:Infinitary Logic and Admissible Sets 375:Stanford Encyclopedia of Philosophy 28:, is a generalization of the usual 408:. You can help Knowledge (XXG) by 281: 257: 191: 170: 123: 14: 392: 313:Ash, C. J.; Knight, J. (2000). 1: 340:; Baldwin, John T. (1985). 308:(PhD). Stanford University. 203:{\displaystyle \Sigma _{1}} 22:Barwise compactness theorem 486: 387: 210:set with parameters from 470:Mathematical logic stubs 287:{\displaystyle \Gamma } 263:{\displaystyle \Gamma } 176:{\displaystyle \Gamma } 129:{\displaystyle \Gamma } 404:-related article is a 344:Model-theoretic logics 288: 264: 244: 224: 204: 177: 157: 130: 106: 86: 62: 36:to a certain class of 289: 265: 245: 225: 205: 178: 158: 156:{\displaystyle L_{A}} 131: 107: 87: 63: 304:Barwise, J. (1967). 278: 254: 234: 214: 187: 167: 140: 120: 96: 76: 52: 38:infinitary languages 112:-finite relational 30:compactness theorem 460:Mathematical logic 402:mathematical logic 284: 260: 250:-finite subset of 240: 220: 200: 173: 163:-sentences, where 153: 126: 102: 82: 58: 18:mathematical logic 417: 416: 338:Feferman, Solomon 243:{\displaystyle A} 223:{\displaystyle A} 105:{\displaystyle A} 85:{\displaystyle L} 61:{\displaystyle A} 34:first-order logic 477: 438: 431: 424: 396: 389: 363: 347: 332: 309: 294:is satisfiable. 293: 291: 290: 285: 269: 267: 266: 261: 249: 247: 246: 241: 229: 227: 226: 221: 209: 207: 206: 201: 199: 198: 182: 180: 179: 174: 162: 160: 159: 154: 152: 151: 135: 133: 132: 127: 111: 109: 108: 103: 91: 89: 88: 83: 67: 65: 64: 59: 485: 484: 480: 479: 478: 476: 475: 474: 445: 444: 443: 442: 385: 370: 360: 352:. p. 295. 350:Springer-Verlag 335: 329: 312: 303: 300: 276: 275: 252: 251: 232: 231: 212: 211: 190: 185: 184: 165: 164: 143: 138: 137: 118: 117: 94: 93: 74: 73: 68:be a countable 50: 49: 46: 12: 11: 5: 483: 481: 473: 472: 467: 462: 457: 447: 446: 441: 440: 433: 426: 418: 415: 414: 397: 383: 382: 369: 368:External links 366: 365: 364: 358: 336:Barwise, Jon; 333: 327: 310: 299: 296: 283: 259: 239: 219: 197: 193: 172: 150: 146: 125: 101: 81: 70:admissible set 57: 45: 42: 24:, named after 13: 10: 9: 6: 4: 3: 2: 482: 471: 468: 466: 463: 461: 458: 456: 453: 452: 450: 439: 434: 432: 427: 425: 420: 419: 413: 411: 407: 403: 398: 395: 391: 386: 381: 377: 376: 372: 371: 367: 361: 359:3-540-90936-2 355: 351: 346: 345: 339: 334: 330: 328:0-444-50072-3 324: 320: 316: 311: 307: 302: 301: 297: 295: 273: 237: 217: 195: 148: 144: 115: 99: 79: 71: 55: 43: 41: 39: 35: 31: 27: 23: 19: 465:Metatheorems 410:expanding it 399: 384: 373: 343: 314: 305: 230:, and every 136:is a set of 47: 21: 15: 272:satisfiable 26:Jon Barwise 449:Categories 298:References 116:. Suppose 282:Γ 258:Γ 192:Σ 171:Γ 124:Γ 44:Statement 319:Elsevier 114:language 274:. Then 356:  325:  92:be an 72:. Let 20:, the 400:This 183:is a 406:stub 354:ISBN 323:ISBN 48:Let 32:for 270:is 16:In 451:: 378:: 348:. 321:. 317:. 437:e 430:t 423:v 412:. 362:. 331:. 238:A 218:A 196:1 149:A 145:L 100:A 80:L 56:A

Index

mathematical logic
Jon Barwise
compactness theorem
first-order logic
infinitary languages
admissible set
language
satisfiable
Elsevier
ISBN
0-444-50072-3
Feferman, Solomon
Model-theoretic logics
Springer-Verlag
ISBN
3-540-90936-2
Stanford Encyclopedia of Philosophy
"Infinitary Logic", Section 5, "Sublanguages of L(ω1,ω) and the Barwise Compactness Theorem"
Stub icon
mathematical logic
stub
expanding it
v
t
e
Categories
Theorems in the foundations of mathematics
Mathematical logic
Metatheorems
Mathematical logic stubs

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