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Pseudo-finite field

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22: 220: 65: 43: 251: 109: 89: 36: 30: 47: 246: 155: 211:, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 11 (3rd revised ed.), 113: 180: 101: 216: 172: 125: 86: 226: 196: 164: 192: 230: 212: 200: 188: 105: 240: 129: 128:
is pseudo-finite and every pseudo-finite field is quasifinite. Every non-principal
93: 176: 136: 184: 168: 15: 153:
Ax, James (1968), "The Elementary Theory of Finite Fields",
8: 96:. This is equivalent to the condition that 207:Fried, Michael D.; Jarden, Moshe (2008), 66:Learn how and when to remove this message 135:Pseudo-finite fields were introduced by 29:This article includes a list of general 163:(2), Annals of Mathematics: 239–271, 7: 132:of finite fields is pseudo-finite. 140: 35:it lacks sufficient corresponding 14: 20: 108:of every positive degree) and 1: 85:is an infinite model of the 110:pseudo algebraically closed 268: 120:has a point defined over 104:(perfect with a unique 50:more precise citations. 156:Annals of Mathematics 215:, pp. 448–453, 252:Field (mathematics) 114:irreducible variety 80:pseudo-finite field 112:(every absolutely 78:In mathematics, a 222:978-3-540-77269-9 159:, Second Series, 126:hyperfinite field 76: 75: 68: 259: 233: 209:Field arithmetic 203: 71: 64: 60: 57: 51: 46:this article by 37:inline citations 24: 23: 16: 267: 266: 262: 261: 260: 258: 257: 256: 237: 236: 223: 213:Springer-Verlag 206: 169:10.2307/1970573 152: 149: 72: 61: 55: 52: 42:Please help to 41: 25: 21: 12: 11: 5: 265: 263: 255: 254: 249: 239: 238: 235: 234: 221: 204: 148: 145: 74: 73: 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 264: 253: 250: 248: 245: 244: 242: 232: 228: 224: 218: 214: 210: 205: 202: 198: 194: 190: 186: 182: 178: 174: 170: 166: 162: 158: 157: 151: 150: 146: 144: 142: 138: 133: 131: 127: 123: 119: 115: 111: 107: 103: 99: 95: 94:finite fields 91: 88: 84: 81: 70: 67: 59: 56:December 2012 49: 45: 39: 38: 32: 27: 18: 17: 247:Model theory 208: 160: 154: 134: 130:ultraproduct 121: 117: 102:quasi-finite 97: 82: 79: 77: 62: 53: 34: 87:first-order 48:introducing 241:Categories 231:1145.12001 201:0195.05701 147:References 124:). Every 31:references 177:0003-486X 106:extension 193:0229613 185:1970573 139: ( 44:improve 229:  219:  199:  191:  183:  175:  90:theory 33:, but 181:JSTOR 116:over 217:ISBN 173:ISSN 141:1968 227:Zbl 197:Zbl 165:doi 143:). 100:is 92:of 243:: 225:, 195:, 189:MR 187:, 179:, 171:, 161:88 137:Ax 167:: 122:F 118:F 98:F 83:F 69:) 63:( 58:) 54:( 40:.

Index

references
inline citations
improve
introducing
Learn how and when to remove this message
first-order
theory
finite fields
quasi-finite
extension
pseudo algebraically closed
irreducible variety
hyperfinite field
ultraproduct
Ax
1968
Annals of Mathematics
doi
10.2307/1970573
ISSN
0003-486X
JSTOR
1970573
MR
0229613
Zbl
0195.05701
Springer-Verlag
ISBN
978-3-540-77269-9

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