Hedman. A First Course in Logic, 2004 (Oxford)

Kim, Byunghan 292, 294 Kirby–Paris theorem 385 Kleene Normal Form 325 Kleene’s Recursion theorem 326 Kleene, Stephen 333

Knight, Robin 294 Kreutzer’s theorem 400 Kreutzer, Stephan 399

L348

L¨ob’s theorem 387 L¨owenhiem–Skolem number 402 L¨owenhiem–Skolem theorems

Downward 169, 405 Upward 167

Lachlan’s theorem 294 Least Fixed-Point Logic 399 length of input 337

LFP 399

limit ordinal 154 Lindstr¨om’s theorem

on extensions of first-order logic 403

o-minimal 246 one-to-one xix

Omitting Types theorem 272 operator 396

order property 291 ordinal number 153 Otter 137

P35

P-resolution 146

P=NP 36, 342, 354, 423 Partial Fixed-point Logic 398 partial isomorphism 393 partial order 197

Peano Arithmetic 360 pebble games 392

Ehrenfeucht–Fraisse game 393 k-pebble game 410

PFP 398

PNF 109 polynomial

space 348

time xiv, 35, 338 time reduction 351

Post, Emile 333 power set 77

prenex normal form 109 prime model 279 primitive recursion 303

primitive recursive functions 304 primitive recursive set 312 primitive symbols 2

projective geometry 202 proof by contradiction 18 Prolog 137

provably equivalent 20 PSPACE 348 Putnam, Hilary 331

quantifier elimination 222 quantifier-free formula 81

random graph 220 realizable 268 recursive

functions 310 set 312

recursively enumerable set 328 recursively inseparable 358 recursively reducible 334 reduct 61

relation xvii relational

database 69 vocabulary 221

resolvent 38, 124 Rice’s theorem 335

Robinson’s Joint Consistency 186 Robinson, Abraham 186

Robinson, John Allen 120 Robinson, Julia 331 Rosser’s theorem 387 Russell, Bertrand 357

Ryll-Nardzewski, Czeslaw 215

T-computable function 318 T-resolution 146

unbounded search 310 uncountable 76 unification 121 Unification algorithm 122 universal formula 85 universal model 283, 285 universal quantifier 54

vocabulary 59

weak Monadic second-order logic 392 well ordered set 153

Well Ordering Principle 156 Whitehead, Alfred North 357 wild theories 293

Wilkie, Alex 247

Zermeleo–Frankel set theory 162

ZFC 162

Zil’ber’s Theorem 210