234 INDEX
Baumgartner example, 141
big type, 97
brimful, 73
brimmed, 73
chain, 27
chain , 76
closed map, 10
coextension, 147
coherence property, 28
coherent chain, 83
collection cardinal, 106
compact galois types, 84
complete sentence, 45
complete sentence, 𝐿𝜔1,𝜔(𝑄), 54
completeness, 159
cotorsion theories, 30
countable closure property, 8
cub, 6
cut-pair, 58
definability of types, 187
determined over, 9
Devlin-Shelah weak diamond, 127
diagram, 50
direct limit, 28
direct union, 28
disjoint amalgamation over limit models,
79
disjoint amalgamation property, 29
dominance lemma, 183
downward closed, 32
EM-set, 50
end extension, 40
end extension sentence, 212
enumeration, 152
excellence, first order, 179
excellence, quasiminimal, 10
excellent, 160
exchange axiom, 3
extendibility sentence, 212
extension lemma, 145
few, 165
filtration, 160
finitary AEC, 184
finite character, AEC, 184
finite diagram, 35
fragment, 5, 211
full, 159
Galois saturated, 69
Galois type, 68, 69
Galois-stable, 71
generalized symmetry, 158
good, 141
good atomic class, 160
good enumeration, 154
good system, 151
group, aqm, 15
Hanf Function, 33
Hanf Number, 33
Hanf Number, AEC, 34
Hanf number, Galois types, 106
Hanf number: categoricity, 117
Hart-Shelah example, 194
hereditary cardinality, 110
homogeneity: ℵ0-over models, 8
homogeneous geometry, 3
homogeneous model theory, 35
homogeneous, sequence, 22
Hrushovski construction, 29
independence, atomic classes, 146
independent family, 125
independent system, 10, 151
inhomogeneity, 21
isomorphic systems, 167
J. Knight example, 138
joint embedding, 29, 64
owenheim-Skolem number, 28
Lachlan example, 193
limit model, 76, 80, 123
linearization, 152
local galois types, 84
Lopez-Escobar theorem, 40
Marcus Example, 22, 139, 142
Martin’s Axiom, 126
maximal model, 123
maximal triple, 57
metric AEC, 36
minimal type, 97
model homogeneous, 67
monster model, 68
Morley omitting types theorem, 205
Morley’s categoricity theorem, 45
Non-elementary class, 26
nonalgebraic, 94
omitting Galois types, 106
omitting types theorem, 33
omitting types: set theoretic method, 111
order property, 116
order type, 73
partial monomorphism, 7
partial type, 33
pregeometry, 3
Presentation Theorem, 30
primary, 141
prime over, 10, 141
proper for linear orders, 50
proper pair, 57
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