Errata

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\begin{document} \maketitle \begin{itemize} \section{Corrections} \item p. vii, l. -3: Should be: type UNIQ341103617ea76558-MathJax-3-QINU..." \item p. 21, Exercise 1.14.5: UNIQ341103617ea76558-MathJax-4-QINU should be UNIQ341103617ea76558-MathJax-5-QINU \item p. 22, l. -12: [70] should be [71] \item p. 23, l. 19: [209] refers to a paper of A. Wilkie, it should refer to George Wilmer's thesis which is missing in the references. \item p. 48, l. 3: the second instance of 2.3.2 should be 2.3.4. \item p. 57, Proof of Corollary 3.1.17. Should be Theorem 3.1.16..." To finish the argument one also needs to evoke Theorem 2.1.1. \item p. 85, Exercise 3.6.17: Delete the hint. \item p.98, l.-3: In the first line of the displayed formula, UNIQ341103617ea76558-MathJax-6-QINU should be replaced by UNIQ341103617ea76558-MathJax-7-QINU . The same change should be made in the second line. \item p.106, paragraph starting with l. -9: Replace the third sentence with: Let UNIQ341103617ea76558-MathJax-8-QINU be the set of meet-irreducibles." Then at the end of the paragraph replace the last part of the last sentence starting with . . . containing UNIQ341103617ea76558-MathJax-9-QINU. . ." with . . . containing UNIQ341103617ea76558-MathJax-10-QINU , which is UNIQ341103617ea76558-MathJax-11-QINU." \item p. 109, Theorem 4.5.5: Definition of UNIQ341103617ea76558-MathJax-12-QINU is missing. Before the theorem insert: If UNIQ341103617ea76558-MathJax-13-QINU and UNIQ341103617ea76558-MathJax-14-QINU are representations, the product UNIQ341103617ea76558-MathJax-15-QINU is a function UNIQ341103617ea76558-MathJax-16-QINU defined by UNIQ341103617ea76558-MathJax-17-QINU iff UNIQ341103617ea76558-MathJax-18-QINU and UNIQ341103617ea76558-MathJax-19-QINU. Then UNIQ341103617ea76558-MathJax-20-QINU and UNIQ341103617ea76558-MathJax-21-QINU." \item p.110/l.15: Should be: UNIQ341103617ea76558-MathJax-22-QINU. \item p.110/l.18: Delete “UNIQ341103617ea76558-MathJax-23-QINU”. \item p. 118, l. 12: Near end of last line of the Theorem, delete the extraneous “) ” \item p.128/Lemma 4.7.4: Interchange “UNIQ341103617ea76558-MathJax-24-QINU” and “UNIQ341103617ea76558-MathJax-25-QINU”. \item p.152/l.21: Expression at end of line should be: UNIQ341103617ea76558-MathJax-26-QINU. \item p. 159, l. -1. UNIQ341103617ea76558-MathJax-27-QINU \item p. 159. Lemma 6.2.5. Delete the last part on the last sentence starting with and if..." \item p. 177, l. -12: UNIQ341103617ea76558-MathJax-28-QINU should be UNIQ341103617ea76558-MathJax-29-QINU \item p. 179, l. -12: [132] should be [130] \item p. 179, l. -8: should [166] be J. Schmerl, Peano models with many generic classes. Pacific Journal of Mathematics 46, 523-536 (1973). This entry is missing in the references. \item p. 182, Proposition 7.1.3: UNIQ341103617ea76558-MathJax-30-QINU is supposed to be just a cut, but it should be also assumed to be closed under addition and multiplication \item p. 246. Lemma 9.4.3 (1). One has to assume that UNIQ341103617ea76558-MathJax-31-QINU and UNIQ341103617ea76558-MathJax-32-QINU are not infimum and supremum of the same gap. \item p. 292, Question 17 is garbled. It should say: Suppose UNIQ341103617ea76558-MathJax-33-QINU is countable recursively saturated and UNIQ341103617ea76558-MathJax-34-QINU is such that UNIQ341103617ea76558-MathJax-35-QINU. Is there a countable recursively saturated UNIQ341103617ea76558-MathJax-36-QINU such that UNIQ341103617ea76558-MathJax-37-QINU, and if UNIQ341103617ea76558-MathJax-38-QINU is coded in UNIQ341103617ea76558-MathJax-39-QINU, then UNIQ341103617ea76558-MathJax-40-QINU? \section{Typos} \item p. vi, l. 7: fragment = fragment of \item p. vi, l. -17: While, = While \item p. vi, l, -9: proves = and proves \item p. vi, l. -2 f.b.: purpose = purpose of \item p. vii, l. -9: delete and" \item p. vii, l. -2 f: For every countable model UNIQ341103617ea76558-MathJax-41-QINU, the isomorphism type if its reducts... \item p. viii, l. -14: the Chapter 7 = Chapter 7 \item p. 1, l. 3: delete a'' \item p. 3, l. -11: is UNIQ341103617ea76558-MathJax-42-QINU = UNIQ341103617ea76558-MathJax-43-QINU is \item p. 3, l. -4: UNIQ341103617ea76558-MathJax-44-QINU = UNIQ341103617ea76558-MathJax-45-QINU \item p. 8, l. -5: UNIQ341103617ea76558-MathJax-46-QINU = UNIQ341103617ea76558-MathJax-47-QINU \item p. 14, Definition 1.9.1: partial inductive satisfaction class''should be in italics \item p. 14, l. -9 and 7: instead of Con(Th(UNIQ341103617ea76558-MathJax-48-QINU) one should read Th(UNIQ341103617ea76558-MathJax-49-QINU is consistent'' \item p. 19, l. 14: proof the = proof of the \item p. 24, l. 13: [69] . = [69]. \item p. 24, l. 17: Kotlarski and Kaye = Kaye and Kotlarski \item p. 25, l. 1: models arithmetic = models of arithmetic \item p.27, l.22: In Corollary 2.1.4, last word of first line should be “end”, not “and”. \item p. 32, l. 7: the contrary = to the contrary \item p. 33, l. -5: replaced = replaced by \item p. 33, l. 4 f.b.: single = a single \item p. 48, l. 15: Wikie = Wilkie \item p. 49, l. -6: each of which = each element of which \item p. 51, l. 7: UNIQ341103617ea76558-MathJax-50-QINU should be UNIQ341103617ea76558-MathJax-51-QINU (similarly for p. 51, l. 9) \item p. 51, l. 17: unboounded = unbounded \item p. 52, l. 21: infinte = infinite \item p. 53, l. 2: type = types \item p. 54, l. 6: do not look = do not look the same \item p. 55, l. 11: the another = another \item p. 57, l. 14: realizes = realize \item p. 57, l. -10: Should be Theorem 3.1.16..." \item p. 57, l. -7; Should be UNIQ341103617ea76558-MathJax-52-QINU... \item p. 58, l. 10: since UNIQ341103617ea76558-MathJax-53-QINU, is rare = , since UNIQ341103617ea76558-MathJax-54-QINU is rare \item p. 60, l. 13: gap(b)UNIQ341103617ea76558-MathJax-55-QINUgap(b) = gap(b) \item p. 60, all UNIQ341103617ea76558-MathJax-56-QINU's in the lines -8,-7, and -6 should be UNIQ341103617ea76558-MathJax-57-QINU's. \item p. 61, l. 3 UNIQ341103617ea76558-MathJax-58-QINU should be UNIQ341103617ea76558-MathJax-59-QINU. \item p. 61, l. -5 : The are = There are \item p. 67, l. -18: types. = types, \item p. 67, l. -17: Then = then \item p. 80, l. 7: UNIQ341103617ea76558-MathJax-60-QINU = UNIQ341103617ea76558-MathJax-61-QINU \item p. 85, Exercise 3.6.25: are = There are \item p. 87, Definition after 3.6.38 should be UNIQ341103617ea76558-MathJax-62-QINU, not UNIQ341103617ea76558-MathJax-63-QINU. \item p. 100, l. 18: Should be UNIQ341103617ea76558-MathJax-64-QINU \item p. 107, l. 3: Theorem 4.5.32 = Corollary 4.5.32 \item p. 107, l. -16: represenatation \item p. 107, l. -3: UNIQ341103617ea76558-MathJax-65-QINU should be UNIQ341103617ea76558-MathJax-66-QINU. \item p. 108, l. 23: be list all = be a list of all \item p. 109. l. 4: Should be The inclusion UNIQ341103617ea76558-MathJax-67-QINU..." \item p. 122, l. -15: used get = used to get \item p. 124, l. 14: hold for = hold for \item p. 125, l. -17: the tree = on the tree \item p. 128, l. -9: represenations \item p. 131, l. 3: (see Exercise 4.8.2) \item p. 133, l. 8: charaterization \item p. 135, l. 7: introduced \item p. 142, l. 1: there some = there exists some \item p. 145, l. 2: instead = instead of ? \item p. 151, l. 17: is not be = is not \item p. 152, l. 17: off = of \item p. 156, l. -18: linearly set = linearly ordered set \item p. 157, l. 17: Theorems 5.3.4 = Theorem 5.3.4 \item p. 162, l. 10,12: Theorem 6.2.6 = Lemma 6.2.6 \item p. 166, l. -10: funtcions \item p. 168, l. -6: would no = would be no \item p. 169, second line of Theorem 6.4.3: UNIQ341103617ea76558-MathJax-68-QINU \item p. 171, l. 10: the proof = of the proof \item p. 173. First line of Theorem 6.4.8: UNIQ341103617ea76558-MathJax-69-QINU. \item p. 177, l. -14: possibilities \item p. 177, l. -5: not = are not \item p. 179, l. -14: independently \item p. 184, l. -4: Propositional = Proposition \item p. 189, l. -11: Theorem 2.2.8 = Theorem 2.2.16 \item p. 191, l.-8: Should be UNIQ341103617ea76558-MathJax-70-QINU \item p. 192, l. 8: if = of \item p. 194, l. -6: Theorembut = Theorem but \item p. 197, l. 12: model IA = model of IA \item p. 200, l. -10: which = which is \item p. 201, l. -12: models = models of \item p. 203, l. 10: UNIQ341103617ea76558-MathJax-71-QINU \item p. 206, l. 10: model = models \item p. 209, Fourth line of the proof of Corollary 8.4.6: UNIQ341103617ea76558-MathJax-72-QINU \item p. 214, l. -17: than least = than the least \item p. 221, l. -12: delete a'' \item p. 222, l. 5: Corollary 3.2.4 = Lemma 3.2.4 \item p. 225, l. 7: maximal = a maximal \item p. 227, l. 12: Corollary 8.1.2 = Proposition 8.1.3. Delete the statement in parenthesis. \item p. 227, l. -10: Back-and-forth, = Back-and-forth \item p. 228, l. 20 f.b.: Frederike = Friederike \item p. 229, l. 9: proof the = proof of the \item p. 229, l. -14: the question mark appears upside down'' \item p. 233, l. 12: aid = and \item p. 234, l. 8: Proposition 9.1.3 = Lemma 9.1.3 \item p. 235, l. 2: models = model \item p. 239, l. 13: index if = index of \item p. 250, l. -6 f: realizes = realize \item p. 253, l. -7: of countable = of a countable \item p. 254, l. 14: definiton \item p. 267, l. -12: devoted the = devoted to the \item p. 268, l. 6: delete an'' \item p. 276, l. -1: Use previous = Use the previous \item p. 280, l. 11: theory = theory of \item p. 284, l. 5: is get = is to get \item Reference [36]: G\"{o}tenborg = G\"{o}teborg \item Reference [43]: add {\it Mathematical Logic and Foundations of Set Theory} (Proc. Internat. Colloq., Jerusalem, 1968)'' \item Reference [54]: add Volume 1292 of {\it Lecture Notes in Mathematics}'' \item Reference [83]: of 619 = 619 of \item Reference [85]: delete (1983)''; this reference should appear after reference [88] \item Reference [109]: od = of \item Reference [113]: of pa = of UNIQ341103617ea76558-MathJax-73-QINU \item Reference [120]: add  in Automorphisms of first-order structures, R. Kaye, D. Macpherson (eds.)'' \item Reference [148]: {\bf CIII} = {\bf 103} \item Reference [153]: charaterization \item Reference [164]: add Volume 859 of {\it Lecture Notes in Mathematics}'' \item Reference [167]: add Stud. Logic Found. Math., 120'' \item Reference [172]: add Lecture Notes Logic, 12'' \item Reference [188]: Unmglichkeit = Unm\"{o}glichkeit; vollstndigen = vollst\"{a}ndigen \item Reference [189]: abzhlbar = abz\"{a}hlbar; Fundam. = Fund. \item Reference [199]: add Volume 834 of {\it Lecture Notes in Mathematics}'' \item Reference [204]: poljak-r\"{o}dl = Poljak-R\"{o}dl \item Reference [206]: the name of the journal is usually abbreviated as Algebra Logic Appl.'' \item Reference [208]: complete = complete models \item Reference [212]: add Proceedings of the International Congress of Mathematicians'' \end{itemize} \end{document}