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