# A Mathematical Introduction to Logic

## Errata to the Second Edition:

Page 14, line 6 from below: The second occurrence of the word "set" should be deleted, so that the phrase reads "an arbitrary set of sentence symbols."

Page 25, about 1/3 down the page: "The more generally applicable a procedure is," delete the spurious "it" after "procedure."

Page 36, Example 3: C* is a class of algebraic functions, but it is not correct to say that "C* is the class of algebraic functions." The class of all algebraic functions (as defined for example in Section 65 of van der Waerden's Modern Algebra) includes more than the ones in Example 3. (Not every polynomial equation is solvable by radicals.)

Page 41, line 16 from below: There should be a bar over the symbol h.

Page 42, lines 3-4: The tag at the right margin should be (*), and not (1.1).

Page 48, line 4: The subscripts on the gammas should go 1, 2, ... , k (and not i, 2, ... , k).
In line 9 from below, there is an X (with an arrow over it) that should be Y (with an arrow over it).

Page 64, line 17 from below: "any any" should be simply "any."

Page 84, line 7 from below: "...for this language...."

Page 97, display (*): The last s should be x . That is, the conclusion should be that B satisfies not-phi with (h o s)(x | h(a)).

Page 100, Exercise 11, part (c): The symbol N should be replaced by a "shadow-cap" letter N.

Page 104, lines 8, 14, and 16: The correct phrase is "real-closed ordered field."

Page 107, line 16: In the first line of the proof of the Unique Readability Theorem for Terms, "iff" should be "if."

Page 117, in the statement of the Generalization Theorem, "do" should be "does."

Page 135, line 10 from below: The spurious "-|" sign should be deleted.

Page 138, line 15 from below: The "if" should be "iff."

Page 168, middle of the page: In the formula pi_S(x,y), the subscript z should be on-line.

Page 169, line 19: The second of the three Fraktur letters in this line should be A instead of B.

Page 170, line 4: Delete the second of the two parentheses just before the conditional symbol.

Page 186, last displayed formula: Delete the second "not," so that the part to the right of the double arrow reads, "not [b is the Gödel number of a formula...."

Page 195, line 15: The two conjunction symbols must be disjunction symbols.

Page 204, the proof of Lemma 33B: The parenthetical material in the first four lines of the proof tacitly appeals to consistency. It seems better simply to replace it by the following: "(Why? Because there can be only one n for which t = S^n 0 is true in N.)"   See also the following correction.

Page 206, line 8: Here "m = n" needs to be negated. (This is where the fact comes in that A_E knows that 80 is different from 87.)

Page 211, line 6: The first symbol should be lightface A, not boldface.

Page 230, line 14 from below: Here "<" should be lightface. There are problems with lightface/boldface parentheses in this line, too.

Page 235, line 14 from below: There is a missing 0 in theta's third argument.

Page 255, line 5: In this line, the equality symbol "=" should be the set-membership symbol.

Page 256, Lemma 36I, part (b): Here "the" should be "then." Similarly in part (c).

Page 264, Exercise 6: Insert "f" after "representing."

Page 274, line 3: Change "sentence a of number theory" to "sentence sigma of number theory".

Page 275, Exercise 1: Replace A_E throughout by PA.

Page 286, last line: Replace the fraktur N by a fraktur A.

Page 287, line 5: In formula (S2), the X should be x.

Page 291, line 17: There is a missing negation symbol in the second formula. The set in question is {forall x P x fx,   forall y not P gy y}.

Page 294, last line: Add a closing brace after T.

Page 297, line 6 from below: The first Q should have a subscript "i-sub-1", not just i.

Page 302, line 10 from below: Change "every f in the n-place relation" to "every f in the n-place function".

Page 304, line 4 of the text: Add ", +" after the < symbol.

Page 310, middle column, line 6: This should read: S^k0     183
Left column, line 10 from below: The "Th" symbol first occurs on page 148 (not page 152).

Cover 4: On the back cover, the publisher refers to me as Editor of The Journal of Symbolic Logic; this is out of date.

For many of these corrections, I am indebted to Professor José Alfredo Amor, of the Universidad Nacional Autónoma de México.