Finite and Algorithmic Model Theory

More documents

Recommendations

Info

London Mathematical Society Lecture Notes series: 379Finite and Algorithmic Model TheoryEdited byJAVIER ESPARZATechnische Universität München, GermanyCHRISTIAN MICHAUXUniversité de Mons, BelgiumCHARLES STEINHORNVassar College, New York, USA
cambridge university pressCambridge, New York, Melbourne, Madrid, Cape Town,Singapore, São Paulo, Delhi, Tokyo, Mexico CityCambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UKPublished in the United States of America by Cambridge University Press, New Yorkwww.cambridge.orgInformation on this title: www.cambridge.org/9780521718202C○ Cambridge University Press 2011This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the writtenpermission of Cambridge University Press.First published 2011Printed in the United Kingdom at the University Press, CambridgeA catalogue record for this publication is available from the British LibraryLibrary of Congress Cataloguing in Publication dataFinite and algorithmic model theory / edited by Javier Esparza, Christian Michaux,Charles Steinhorn.p. cm. – (London Mathematical Society lecture note series ; 379)Includes index.ISBN 978-0-521-71820-2 (pbk.)1. Finite model theory. 2. Computer science – Mathematics. I. Esparza, Javier.II. Michaux, Christian. III. Steinhorn, Charles. IV. Title. V. Series.QA9.7.F565 2011511.3 ′ 4 – dc22 2010048062ISBN 978-0-521-71820-2 PaperbackCambridge University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred toin this publication, and does not guarantee that any content on suchwebsites is, or will remain, accurate or appropriate.
Page 2 and 3: LONDON MATHEMATICAL SOCIETY LECTURE
Page 6: ContentsPrefaceJavier Esparza, Chri
Page 9 and 10: viiiPrefaceboth theoretically and i
Page 11 and 12: xPrefacea fixed value k such that o
Page 14 and 15: 1Automata-based presentations ofinf
Page 16 and 17: Automata-based presentations of inf
Page 19 and 20: 6 Vince Bárány, Erich Grädel and
Page 21 and 22: 8 Vince Bárány, Erich Grädel and
Page 23 and 24: 10 Vince Bárány, Erich Grädel an
Page 55 and 56:
42 Vince Bárány, Erich Grädel an
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
78 Bart Kuijpers and Jan Van den Bu
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
100 Bart Kuijpers and Jan Van den B
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
110 Vera Koponenpebble game which d
Page 125 and 126:
112 Vera KoponenDefinition 3.2.1 (i
Page 127 and 128:
114 Vera KoponenFact 3.2.5 For any
Page 129 and 130:
116 Vera KoponenAssumption 3.3.3For
Page 131 and 132:
118 Vera KoponenLet π : ω 3 →
Page 133 and 134:
120 Vera Koponen3.4 StabilityNow we
Page 135 and 136:
122 Vera KoponenNext we state the c
Page 137 and 138:
124 Vera Koponen3.5 Recursive bound
Page 139 and 140:
126 Vera KoponenProof. Suppose that
Page 141 and 142:
128 Vera Koponenor [32] for example
Page 143 and 144:
130 Vera Koponenunder subformulas.
Page 145 and 146:
132 Vera Koponeni
Page 147 and 148:
134 Vera KoponenDefinition 3.7.4 We
Page 149 and 150:
136 Vera KoponenTheorem 3.7.7 Suppo
Page 151 and 152:
References[1] J. Baldwin, Finite an
Page 153 and 154:
4Definability in classes of finite
Page 155 and 156:
142 Dugald Macpherson and Charles S
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
References[1] G. Ahlbrandt, M. Zieg
Page 189 and 190:
Page 191 and 192:
178 Stephan Kreutzeron any class of
Page 193 and 194:
180 Stephan Kreutzerintroduction to
Page 195 and 196:
182 Stephan Kreutzer• • • •
Page 197 and 198:
184 Stephan KreutzerindependentsetW
Page 199 and 200:
186 Stephan Kreutzerby definition,
Page 201 and 202:
188 Stephan Kreutzernumber of free
Page 203 and 204:
190 Stephan Kreutzer¬X i by x i =
Page 205 and 206:
192 Stephan Kreutzerof the polynomi
Page 207 and 208:
194 Stephan KreutzerIn this section
Page 209 and 210:
196 Stephan Kreutzertree-decomposit
Page 211 and 212:
198 Stephan Kreutzer(i) If e := {s,
Page 213 and 214:
200 Stephan KreutzerDefinition 5.3.
Page 215 and 216:
202 Stephan Kreutzerdepending on k.
Page 217 and 218:
204 Stephan Kreutzerλ(t)It is easi
Page 219 and 220:
206 Stephan Kreutzerbeing decompose
Page 221 and 222:
208 Stephan KreutzerThis completes
Page 223 and 224:
210 Stephan KreutzerIf there is suc
Page 225 and 226:
212 Stephan Kreutzer1 23 456 7 8910
Page 227 and 228:
214 Stephan KreutzerIt is easily se
Page 229 and 230:
216 Stephan Kreutzerabstractbranchd
Page 231 and 232:
218 Stephan Kreutzer3. A graph has
Page 233 and 234:
220 Stephan KreutzerThe relevant ma
Page 235 and 236:
222 Stephan KreutzerThe formula ϕ
Page 237 and 238:
224 Stephan Kreutzerwith bounded tr
Page 239 and 240:
226 Stephan KreutzerFigure 5.9 Imag
Page 241 and 242:
228 Stephan Kreutzernecessarily hav
Page 243 and 244:
230 Stephan KreutzerFigure 5.11 A w
Page 245 and 246:
232 Stephan KreutzerFigure 5.14 Vor
Page 247 and 248:
234 Stephan Kreutzerthe (at most 3)
Page 249 and 250:
236 Stephan Kreutzerp-Rooted-MinorI
Page 251 and 252:
238 Stephan Kreutzer13 213 24 114 1
Page 253 and 254:
240 Stephan KreutzerobstructionO(C)
Page 255 and 256:
242 Stephan KreutzerCorollary 5.5.1
Page 257 and 258:
244 Stephan KreutzerWe start by sho
Page 259 and 260:
246 Stephan Kreutzerall structures
Page 261 and 262:
248 Stephan KreutzerFigure 5.17 Alg
Page 263 and 264:
250 Stephan Kreutzerloc f (G, r)Def
Page 265 and 266:
252 Stephan KreutzerNote that graph
Page 267 and 268:
254 Stephan Kreutzeras they only co
Page 269 and 270:
256 Stephan KreutzerL(λ, µ). The
Page 271 and 272:
258 Stephan Kreutzerbecomes tractab
Page 273 and 274:
260 Stephan Kreutzerwe must also be
Page 275 and 276:
262 Stephan Kreutzerdefinition of t
Page 277 and 278:
264 Stephan Kreutzereff. somew. den
Page 279 and 280:
References[1] I. Adler, M. Grohe, a
Page 281 and 282:
268 Stephan Kreutzer[32] F. Dorn, F
Page 283 and 284:
270 Stephan Kreutzer[72] C. Papadim
Page 285 and 286:
272 Martin Ottomodel theory as well
Page 287 and 288:
274 Martin Ottocompleteness results
Page 289 and 290:
276 Martin Ottoby the observable co
Page 291 and 292:
278 Martin OttoHypergraphs, which a
Page 293 and 294:
280 Martin Ottotranslation that ass
Page 295 and 296:
282 Martin OttoIn a straightforward
Page 297 and 298:
284 Martin OttoAs formula complexit
Page 299 and 300:
286 Martin OttoA ′ are clear from
Page 301 and 302:
288 Martin Ottocan choose his chall
Page 303 and 304:
290 Martin OttoIn the more interest
Page 305 and 306:
292 Martin OttoA 0 |= ϕ[a]. By inv
Page 307 and 308:
294 Martin Ottoimplications see [23
Page 309 and 310:
296 Martin Ottoguarded subsets and
Page 311 and 312:
298 Martin OttoIt is clear that the
Page 313 and 314:
300 Martin Ottoglobal bisimulation
Page 315 and 316:
302 Martin Ottoa fragment associate
Page 317 and 318:
304 Martin OttoFor Gaifman’s theo
Page 319 and 320:
306 Martin OttoIf n 0
Page 321 and 322:
308 Martin OttoObservation 6.3.2 Fo
Page 323 and 324:
310 Martin OttoLocally acyclic bisi
Page 325 and 326:
312 Martin OttoThis follows from th
Page 327 and 328:
314 Martin Ottocases also provide a
Page 329 and 330:
316 Martin Ottocharacterisations of
Page 331 and 332:
318 Martin Ottotarget node â n in
Page 333 and 334:
320 Martin OttoAmong the long open
Page 335 and 336:
322 Martin Ottoby a hypergraph ˆ H
Page 337 and 338:
324 Martin Ottosize 3. We return to
Page 339 and 340:
326 Martin Ottocondition (ii) rules
Page 341 and 342:
328 Martin Ottostructures of bounde
Page 343 and 344:
330 Martin OttoFO data and combined
Page 345 and 346:
332 Martin OttoThese are proved cla
Page 347 and 348:
334 Martin Ottominimal if their ric
Page 349 and 350:
336 Martin Ottomeaning that every s
Page 351 and 352:
338 Martin Ottodevelopment and rami
Page 353 and 354:
340 Martin Otto[14] Dawar, A., and
show all

Finite and Algorithmic Model Theory

Create successful ePaper yourself

Delete template?

Save as template?