Here is a list of the errors in Marker’s book I have found over the years which are not listed on his errata page (from 2014!) by page/line.


9/3: m_R should be n_R; in the next line, m_j should be m_R, and in the line above, n should be n_R

19/5: x_a1 should read x_1; the statement of part b) also seems false?

19/-10: missing space after that

22/-15: say that D_n is closed under permutation of variables (I think you need this)

24/10: it would be helpful here to say explicitly that you require the function to be N to X and not N to X/E (which you call “interpretable” later at 27/-2)

28/-13 and -11: N needs to be subscripted with i_1 through i_n; last N^{s_0} shoudl be N_{i_0}

29/Exercise 1.4.1: Technically, one needs to handle the case S = empty set separately!

46/-9: N should read |N|

47/1: abar in N

51/-13: delete second \neg

54/15: has no function symbols

56/19: "elements of poor man's bold N" should be "elements of regular N"

56/2nd half of page: 3^{n-m} should read 3^{n-m+1} multiple times until the end of the proof

54/17 and 18: this s does not have to be the same s as in line 16

60/-20 and -18: Archimedean

60/-18: last w should be x?

62/-10: s is a bijection from U onto U

63/-17: why are there no finite models, or models of size < |L|?

65/-18: psi_0, psi_1

65/-11: does not occur in theta_s and set theta_{s+1}

67/8: also require P(c_i)

68/-8: from Section 2.2

73/-17: By Lemma 3.1.2

74/-4: missing {}

76/7: psi (twice)

76/10 and 16: m is used twice in different meanings

76/-13 b is missing after each -h_i/m'_i

77/3: also ~ (h_0,m_0)

78/-9: missing “if”

78/-1: script M should be T

80/12: w_i should read v_i, and v should read w, twice

82/-12: rightarrow should be leftarrow

82/-11: rightarrow should be leftrightarrow

86/-12: “then” is unclear in this proof

86/-9: why X=Y here? not clear

86/-6: why are there such p and q? not clear

86/-4 through -1: should be X intersect Y

88/-7: I \neq intersection_{j in J} P_j

88/-3: missing space after that

89/-12 and -8: n used in two different meanings (also 90/9)

89/-3: K is a model of ACF

90/1: xbar should be vbar twice

90/8: closure of B should be "closure of union of K_0 and B

90/15 and 16: abar should be bbar twice

90/19: conjunction should be disjunction

90/-13: stress that A is any SET

92/1: is this really the same abar?

93/4: “By Lemma 3.2.16” is unclear here

93/7: wbar should be ybar

95/-10: a, b in F

96/11: a>0

96/-14: fraction field of D

97/6: phi: F to F

97/15: Xbar

100/-3: missing parentheses after \exists y

100/-1: By Lemma 3.3.24

101/9: add “in X” before “}”

101/8: use f in place of F

103/-9: f_n: A_n union … union A_N to F

105/16: phi_p: G/p^nG to Z/p^nZ 

105/18: least positive element 1

105/-7: M and N are models of T

106/-10: x should be a twice; also assume b in X

106/-6: need A algebraically closed here

107/18: which n?

107/-10 and -4: abar should be f(abar) twice

107/-1: cbar should be vbar

108/-9: end of line should read x <_1 y and y <_2 x

118/3: add "extending f" at end of line

118/-5: g should read g_i

119/-12 and -7: calN is used twice in different meanings

120/14: Thus, the map is continuous.

123/10: q used here and again later, in different meaning

124/-11: add “in p” before “}”

126/-5: e_0 should be e_1

129/-18 through -12: these lines can be cut?

130/-10: w should be wbar

131/-18: + is not great notation here

131/-4: 3i+2; i is used in two meanings here and the next line

132/-13: phi(f|0)

137/11: l should read let

137/14: bbar should read b

137/-10: Th_B?

138/-13: S^calM_{n-1}(A); \exists v (phi(v_1, …, v_{n_1},v)

139/1 and 14: be consistent about countably vs. countable saturated

139/-8: calM_{alpha+1}

141/5: calN should poo150/-r man’s bold N

141/7: has no countable saturated model

141/-18: n=1???

141/-1: first |A| should read A

142/-20: calM_{lambda^+}

143/1: |\rm M_alpha|

143/-10: calM should be calN

144/8: delete parentheses

146/-3 and -2: n used twice

147/3: vbar should be abar

149: missing {}

149/-10: a^n should be a^(n) (similarly 150/7 and 8)

150/3: of minimal degree in X^(n)

150/-2: f used twice

151/7: missing {

152/21 and 23: mbar_0 is mbar

153: (M_0, N_0) should read (N_0, M_0)

152/-10: delete line

154/9: need |M| = |N|

156/-9: \neg phi_i

158/8: this seems wrong, you need their differences not divisible by p_i?

162/11 and 12: these two lines seem not needed

163/-17 and -16: tp(bbar/A) and tp(cbar/A) instead of tp(abar/A) and tp(bbar/A); c_i > a instead of c_i < a

164/-10: Lemmas

166/-2: the calM_i are a countable chain!

171/-5: delete space after Orey

176/-12 and -8: X is used twice

179/5: add “for all phi”

181/14: tp(X)

171/Lemma 5.2.6: why did you switch from Y,X to J,I?

182/-12: spell out “in”

183/1: too many “if” and “if and only if” to parse

184/13: move } to end of line

184/19: I should be X

202/14: any countably infinite

202/-10: Hint: (Leftarrow)

209/-6 and -1, 210/5 and 8: n used in two different meanings

211/-16: delete “transcendence” twice

218/1: phi is any L_M-formula

220/19: add “for some such psi”

220/-3: dotless jhat

222/-15 and 223/-4: poor man’s bold M

222/-1: X is A-definable

223/16: I suggest letting deg(abar)=1

324/12: -1 = …