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Modus Ponens, 15, 43
for all, 25
MP, 15, 43
formula, 7, 27
atomic, 7, 27
natural deductive logic, 1
unique readability, 10, 32
non-standard model, 53, 55
free variable, 29
of the real numbers, 55
function, 24, 31, 33, 35
not, 2, 7, 25
k-place, 24, 25
or, 2, 9
generalization, 42
Generalization Theorem, 45, 83 parentheses, 7, 24
on Constants, 45 conventions, 9, 30
gothic characters, 33 doing without, 8
graph, 52 power set, 79
Greek characters, 7, 28, 81 predicate, 24, 25
predicate logic, 7
if and only if, 9 premiss, 16, 43
if . . . then, 2, 7, 25 proof, 16, 43
implies, 14, 38 propositional logic, 2, 7
inconsistent, 19, 47 proves, 16, 43
independent set, 52 punctuation, 7, 25
inference rule, 15
in¬nite, 80 quanti¬er
In¬nite Ramsey™s Theorem, 53 existential, 30
in¬nitesimal, 55 scope of, 30
intersection, 79 universal, 24, 25, 30
INDEX 89

Ramsey number, 53 witnesses, 48
Word, 80
Ramsey™s Theorem, 53
In¬nite, 53
relation, 24, 31, 33
k-place, 24, 25, 79
binary, 25, 80
rule of inference, 15, 43

satis¬able, 13, 37
satis¬es, 13, 36, 37
scope of a quanti¬er, 30
sentence, 29
sentential logic, 7
set theory, 79
Soundness Theorem, 19, 47, 83
structure, 33
subformula, 10, 29
subgraph, 52
subset, 79
substitutable, 41
substitution, 41
symbols, 7, 24
logical, 24
non-logical, 24

tautology, 13, 38
term, 26, 31, 35
unique readability, 32
theorem, 31
theory, 39, 45
there is, 2
truth
assignment, 11
in a structure, 36, 37
table, 12, 13
values, 11

uncountable, 80
union, 79
unique readability
of formulas, 10, 32
of terms, 32
Unique Readability Theorem, 10, 32
universal quanti¬er, 30
universe, 33

variable, 24, 31, 34, 35
bound, 29
free, 29
vertex, 52

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