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Takeuti's conjecture

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230: 173: 62:(Prawitz 1968) and Takahashi (Takahashi 1967) by a similar technique (Takahashi 1967), although Prawitz's and Takahashi's proofs are not limited to second-order logic, but concern 139: 295: 214: 271: 300: 86: 207: 106: 123: 264: 200: 82: 40: 290: 153:, 23:39–96. An errata to this article was published in the same journal, 24:149–156, 1954. 305: 90: 257: 180: 63: 36: 85:
in the sense that each of the statements can be derived from each other in the weak system of
70: 32: 130: 48: 52: 241: 184: 284: 146: 28: 118: 59: 20: 156:
Moto-o Takahashi, 1967. A proof of cut-elimination in simple type theory. In
51:, using a semantic technique for proving cut-elimination, based on work by 229: 94: 74: 172: 134: 237: 81:
Takeuti's conjecture is equivalent to the 1-consistency of
245: 188: 137:'s Hauptsatz for second order predicate logic. In 73:'s syntactic proof of strong normalization for 149:, 1953. On a generalized logic calculus. In 265: 208: 140:Bulletin of the American Mathematical Society 8: 43:(Takeuti 1953). It was settled positively: 121:, 1968. Hauptsatz for higher order logic. 272: 258: 215: 201: 7: 226: 224: 169: 167: 133:, 1966. A nonconstructive proof of 87:primitive recursive arithmetic (PRA) 14: 296:Conjectures that have been proved 228: 171: 151:Japanese Journal of Mathematics 89:. It is also equivalent to the 1: 158:Japanese Mathematical Society 244:. You can help Knowledge by 187:. You can help Knowledge by 322: 223: 166: 124:Journal of Symbolic Logic 301:Mathematical logic stubs 107:Hilbert's second problem 93:of the Girard/Reynold's 83:second-order arithmetic 16:Theorem in formal logic 240:-related article is a 183:-related article is a 69:It is a corollary of 33:sequent formalisation 27:is the conjecture of 91:strong normalization 25:Takeuti's conjecture 143:, 72:980–983. 127:, 33:452–457, 1968. 64:higher-order logics 181:mathematical logic 37:second-order logic 253: 252: 196: 195: 160:, 10:44–45. 58:Independently by 313: 274: 267: 260: 232: 225: 217: 210: 203: 175: 168: 71:Jean-Yves Girard 321: 320: 316: 315: 314: 312: 311: 310: 281: 280: 279: 278: 222: 221: 164: 131:William W. Tait 115: 103: 41:cut-elimination 17: 12: 11: 5: 319: 317: 309: 308: 303: 298: 293: 283: 282: 277: 276: 269: 262: 254: 251: 250: 233: 220: 219: 212: 205: 197: 194: 193: 176: 162: 161: 154: 144: 128: 114: 111: 110: 109: 102: 99: 79: 78: 67: 56: 15: 13: 10: 9: 6: 4: 3: 2: 318: 307: 304: 302: 299: 297: 294: 292: 289: 288: 286: 275: 270: 268: 263: 261: 256: 255: 249: 247: 243: 239: 234: 231: 227: 218: 213: 211: 206: 204: 199: 198: 192: 190: 186: 182: 177: 174: 170: 165: 159: 155: 152: 148: 147:Gaisi Takeuti 145: 142: 141: 136: 132: 129: 126: 125: 120: 117: 116: 112: 108: 105: 104: 100: 98: 96: 92: 88: 84: 76: 72: 68: 65: 61: 57: 54: 50: 46: 45: 44: 42: 38: 34: 30: 29:Gaisi Takeuti 26: 22: 291:Proof theory 246:expanding it 235: 189:expanding it 178: 163: 157: 150: 138: 122: 80: 55:(Tait 1966); 24: 18: 306:Logic stubs 119:Dag Prawitz 66:in general; 21:mathematics 285:Categories 113:References 101:See also 95:System F 75:System F 135:Gentzen 60:Prawitz 53:Schütte 31:that a 238:logic 236:This 179:This 242:stub 185:stub 49:Tait 39:has 47:By 35:of 19:In 287:: 97:. 23:, 273:e 266:t 259:v 248:. 216:e 209:t 202:v 191:. 77:.

Index

mathematics
Gaisi Takeuti
sequent formalisation
second-order logic
cut-elimination
Tait
Schütte
Prawitz
higher-order logics
Jean-Yves Girard
System F
second-order arithmetic
primitive recursive arithmetic (PRA)
strong normalization
System F
Hilbert's second problem
Dag Prawitz
Journal of Symbolic Logic
William W. Tait
Gentzen
Bulletin of the American Mathematical Society
Gaisi Takeuti
Stub icon
mathematical logic
stub
expanding it
v
t
e
Stub icon

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