Building Models by Games

Introduction v Preliminaries 1(16) Pictures 1(4) Model theory 5(12) References 16(1) Games and Forcing 17(18) A way of building models 17(6) Games 23(4) Forcing 27(8) References 34(1) Existential Closure 35(48) Adjunction of elements 36(11) Existentially closed models 47(12) E.c. groups 59(13) Robinson forcing 72(11) References 80(3) Chaos or Regimentation 83(49) Mass production 84(11) Atomic models 95(10) Finite-generic models 105(6) E.c. nilpotent groups of class 2 111(21) References 130(2) Classical Languages 132(38) Classical omitting types 133(11) Set-theoretical interruption: unbounded subsets 144(8) Saturation 152(18) References 167(3) Proper Extensions 170(41) Largeness properties 171(14) Definable ultrapowers 185(10) Uncountable boolean algebras 195(16) References 209(2) Generalised Quantifiers 211(39) L(Q) 212(11) Omitting types in L(Q) 223(12) Magidor-Malitz quantifiers 235(15) References 248(2) L(Q) in Higher Cardinalities 250(25) There is a problem 251(9) Completeness and omitting types 260(15) References 273(2) List of types of forcing 275(1) List of open questions 276(6) Bibliography 282(21) Index 303