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    Makowsky, J.A. and Shelah, S. 1983. Positive results in abstract model theory: a theory of compact logics. Annals of Pure and Applied Logic, Vol. 25, Issue. 3, p. 263.

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Book description

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the eighth publication in the Perspectives in Logic series, brings together several directions of work in model theory between the late 1950s and early 1980s. It contains expository papers by pre-eminent researchers. Part I provides an introduction to the subject as a whole, as well as to the basic theory and examples. The rest of the book addresses finitary languages with additional quantifiers, infinitary languages, second-order logic, logics of topology and analysis, and advanced topics in abstract model theory. Many chapters can be read independently.

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See also: Danhof, K. J. and Biichi, J. R. 1973.
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See also: Cole, J. C. and Dickmann, M. A. 1972.
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See also: Barwise, K. J. and Eklof, P. C. 1969; Barwise, K. J. and Eklof, P. C. 1970.
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See also: Barwise, K. J. and Fisher, E. R. 1970; Eklof, P. C. and Fisher, E. R. 1972.
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Flum, J. 1971b Ganzgeschlossene und prddikatengeschlossene Logiken, II. Archiv für Mathematische Logik und Grundlagenforschung, vol. 14 (1971), pp. 99-107.
Flum, J. 1971c A remark on infinitary languages. Journal of Symbolic Logic, vol. 36 (1971), pp. 461-462.
Flum, J. 1972a Die Automorphismenmengen der Modelle einer L Q-Theorie. Archiv für Mathematische Logik und Grundlagenforschung, vol. 15 (1972), pp. 83-85.
Flum, J. 1972b Hanf numbers and well-ordering numbers. Archiv für Mathematische Logik und Grundlagenforschung, vol. 15 (1972), pp. 164-178.
Flum, J. 1975a L(Q)-preservation theorems. Journal of Symbolic Logic, vol. 40 (1975), pp. 410-418.
Flum, J. 1975b First-order logic and its extensions. In: ISILC Logic Conference, edited by Müller, G. H., Oberschelp, A. and Potthoff, K.. Springer-Verlag Lecture Notes in Mathematics, vol. 499 (1975), pp. 248-310.
Flum, J. 1984 Model Itheorie - topologische Modelltheorie. Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 86 (1984), pp. 69-82.
See also: Ebbinghaus, H. D. and Flum, J. 1974; Ebbinghaus, H. D., Flum, J. and Thomas, W. 1984.
Flum, J. and Ziegler, M. 1980 Topological Model Theory. Springer-Verlag Lecture Notes in Mathematics, vol. 769, 1980, x+151 pp.
Fraïssé, R. 1954a Sur l'extension aux relations de quelques propriétés des ordres. Annales Scientifiques de l’École Normale Supérieure, vol. 71 (1954), pp. 363-388.
Fraïssé, R. 1954b Sur quelques classifications des systèmes des relations. Publications Scientifiques de l'Université d'Alger. Série A, vol. 1 (1954), pp. 35-182.
Fraïssé, R. 1955a Sur quelques classifications des relations basées sur des isomorphismes restreints, I: Étude générale. Publications Scientifiques de l'Université d'Alger. Série A, vol. 2 (1955), pp. 15-60.
Fraïssé, R. 1955b Sur quelques classifications des relations basées sur des isomorphismes restreints, II: Applications aux relations d'ordre, et construction d'exemples montrant que ces classifications sont distinctes. Publications Scientifiques de l'Université d'Alger. Série A, vol. 2 (1955), pp. 273-295.
Fraïssé, R. 1956a Sur quelques classifications des relations basées sur des isomorphismes restreints, HI: Comparison des parentés introduites dans la première partie avec des parentés précédemment étudiées. Publications Scientifiques de l'Universite d'Alger. Serie A, vol. 3 (1956), pp. 143-159.
Fraïssé, R. 1956b Étude de certains opérateurs dans les classes de relations, définis a partir d'isomorphismes restreints. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 2 (1956), pp. 59-75.
Fraïssé, R. 1974 Isomorphisme local et équivalence associes à un cardinal; utilité en cal-cul des formules infinies à quanteurs finis. In: Proceedings of the Tarski Symposium, edited by Henkin, L. A.. American Mathematical Society Proceedings of Symposia in Pure Mathematics, vol. 25 (1974), pp. 241-254.
Frayne, T. E., Morel, A. C. and Scott, D. S. 1962 Reduced direct products. Fundamenta Mathematicae, vol. 51 (1962), pp. 195-228.
Friedman, H. M. 1970a Why first-order logic? Manuscript, Stanford University and the University of Wisconsin, 1970, 16 pp.
Friedman, H. M. 1970b Conceptual guide to “Why first-order logic?”. Manuscript, Stanford University and the University of Wisconsin, 1970, 4 pp.
Friedman, H. M. 1971a Back and forth, L(Q), Loou;(Q) and Bethfs theorem. Manuscript, Stanford University, 1971.
Friedman, H. M. 1971b The Beth and Craig theorems in infinitary languages. Manuscript, University of Wisconsin, 1971, 37 pp.
Friedman, H. M. 1971 Beth's theorem in cardinality logics. Israel Journal of Mathematics, vol. 14 (1973), pp. 205-212.
Friedman, H. M. 1974 On existence proofs of Hanf numbers. Journal of Symbolic Logic, vol. 39 (1974), pp. 318-324.
Friedman, H. M. 1975a Adding propositional connectives to countable infinitary logic. Mathematical Proceedings of the Cambridge Philosophical Society, vol. 77 (1975), pp. 1-6.
Friedman, H. M. 1975b Large models of countable height. Transactions of the American Mathematical Society, vol. 201 (1975), pp. 227-239.
Friedman, H. M. 1975c One hundred and two problems in mathematical logic. Journal of Symbolic Logic, vol. 40 (1975), pp. 113-129.
Friedman, H. M. 1977 Adding propositional connectives to countable infinitary logics. Mathematical Proceedings of the Cambridge Philosophical Society, vol. 77 (1977), pp. 1-6.
Friedman, H. M. 1978 On the logic of measure and category I. Manuscript, Ohio State University, 1978, 13 pp.
Friedman, H. M. 1979a Addendum to “On the logic of measure and category I”. Manuscript, Ohio State University, 1979, 8 pp.
Friedman, H. M. 1979b Borel structures in mathematics I. Manuscript, Ohio State University, 1979, 9 pp.
Friedman, H. M. 1979c On the naturalness of definable operations. Houston Journal of Mathematics (Houston, Texas), vol. 105 (1979), pp. 325-330.
Friedman, H. M. and Jensen, R. B. 1968 Note on admissible ordinals. In: The Syntax and Semantics of Infinitary Languages, edited by Barwise, K. J.. Springer-Verlag Lecture Notes in Mathematics, vol. 72 (1968), pp. 77-79.
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Friedman, S. D. 1982a Steel forcing and Barwise compactness. Annals of Mathematical Logic, vol. 22 (1982), pp. 31-46.
Friedman, S. D. 1982b Uncountable admissibles, I: Forcing. Transactions of the American Mathematical Society, vol. 270 (1982), pp. 61-73.
Friedman, S. D. 1984 Model theory for L∞ω1 . Annals of Pure and Applied Logic, vol. 26 (1984), pp. 103-122.
Friedman, S. D. and Shelah, S. 1983 Tall α-recursive structures. Proceedings of the American Mathematical Society, vol. 88 (1983), pp. 672-678.
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Georgis, Z. II. 1984 Malitz quantifiers and well orderings. Journal of Symbolic Logic, vol. 49 (1984), pp. 691-692. Abstract.
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See also: Erdos, P., Gillman, L. and Henriksen, M. 1955.
Giorgetta, D. and Shelah, S. 1984 Existentially closed structures in the power of the continuum. Annals of Pure and Applied Logic, vol. 26 (1984), pp. 123-148.
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Gurevich, Y. 1979a Modest theory of short chains, I. Journal of Symbolic Logic, vol. 44 (1979), pp. 481-490.
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Gurevich, Y. 1982 Crumbly spaces. In: Logic, Methodology and Philosophy of Science VI, edited by Cohen, L. J., Loś, J., Pfeiffer, H. and Podewski, K.-P.. North-Holland Publishing Company, 1982, pp. 179-191.
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See also: Gurevich, Y. and Harrington, L. A. 1982.
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See also: Hauschild, K. and Herre, H. 1976; Wolter, H. and Herre, H. 1977.
Herre, H. and Pinus, A. G. 1978 Zum Entscheidungsproblem für Theorien in Logiken mit monad- ischen verallgemeinerten Quantoren. Zeitschrift für Mathema- tische Logik und Grundlagen der Mathematik, vol. 24 (1978), pp. 375-384.
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See also: Donder, H.-D., Jensen, R. B. andKoppelberg, B. J. 1981; Friedman, H. M. and Jensen, R. B. 1968.
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See also: Solovay, R. M., Reinhardt, W. N. and Kanamori, A. 1978.
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See also: Jensen, R. B. and Karp, C. 1971.
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Kaufmann, M. J. 1978b Some results in stationary logic. Journal of Symbolic Logic, vol. 43 (1978), pp. 369-370. Abstract.
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See also: Barwise, K. J., Kaufmann, M. J. and Makkai, M. 1978; Barwise, K. J., Kaufmann, M. J. and Makkai, M. 1981; Cutland, N. J. and Kaufmann, M. J. 1979; Cutland, N. J. and Kaufmann, M. J. 1980; Shelah, S. and Kaufmann, M. J. 198?a; Shelah, S. and Kaufmann, M. J. 198?b.
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See also: Bruce, K. B. and Keisler, H. J. 1979; Chang, C. C. and Keisler, H. J. 1962; Chang, C. C. and Keisler, H. J. 1973; Chang, C. C. and Keisler, H. J. 1977; Hoover, D. N. and Keisler, H. J. 1984.
Keisler, H.J. and Morley, M.D. 1967 On the number of homogeneous models of a given power. Israel Journal of Mathematics, vol. 5 (1967), pp. 73-78.
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Kierstead, H. A. and Remmel, J. B. 1983 Indiscernibles and decidable models. Journal of Symbolic Logic, vol. 48 (1983), pp. 21-32.
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See also: Myhill, J. and Kino, A. 1975.
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See also: Feferman, S. and Kreisel, G. 1966; Simpson, S. G., Kreisel, G. and Mine, G.E. 1975.
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See also: Barwise, K. J. and Makkai, M. 1976; Barwise, K. J., Kaufmann, M. J. and Makkai, M. 1978; Barwise, K. J., Kaufmann, M. J. and Makkai, M. 1981; Harnik, V. and Makkai, M. 1976; Harnik, V. and Makkai, M. 1977; Harnik, V. and Makkai, M. 1979; Harrington, L. A., Makkai, M. and Shelah, S. 198?.
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See also: Mahr, B. and Makowsky, J.A. 1983a; Mahr, B. and Makowsky, J.A. 1983b; Mahr, B. and Makowsky, J. A. 1984.
Makowsky, J.A. and Marcja, A. 1977 Problemi di decidibilità in logica topologica. Rendiconti del Sem-inario Matematico dell'Università di Padova, vol. 56 (1977), pp. 67-68.
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See also: Baumgartner, J. E., Malitz, J. J. and Reinhardt, W. N. 1970; Magidor, M. and Malitz, J. J. 1977a; Magidor, M. and Malitz, J. J. 1977b.
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See also: Eklof, P. C. and Mekler, A. H. 1979; Eklof, P. C. and Mekler, A. H. 1981; Eklof, P. C. and Mekler, A. H. 1982.
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See also: Baldwin, J. T. and Miller, D. E. 1982; Burgess, J. P. and Miller, D. E. 1975.
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See also: Keisler, H. J. and Morley, M. D. 1967; Keisler, H. J. and Morley, M. D. 1968.
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See also: Doner, J. E., Mostowski, A. and Tarski, A. 1978; Ehren-feucht, A. and Mostowski, A. 1956; Grzegorczyk, A., Mostowski, A. and Ryll-Nardzewski, C. 1961; Kuratowski, K. and Mostowski, A. 1968; Ku-ratowski, K. and Mostowski, A. 1976; Marek, W. and Mostowski, A. 1975; Tarski, A., Mostowski, A. and Robinson, R. M. 1953.
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See also: Lee, V. and Nadel, M. E. 1977; Lipshitz, L. M. and Nadel, M. E. 1978.
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Shelah, S. 1975a A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals. Israel Journal of Mathematics, vol. 21 (1975), pp. 319-349.
Shelah, S. 1975b A two-cardinal theorem. Proceedings of the American Mathematical Society, vol. 48 (1975), pp. 207-213.
Shelah, S. 1975c Categoricity in א1 of sentences in Lω1ω(Q). Israel Journal of Mathematics, vol. 20 (1975), pp. 127-148.
Shelah, S. 1975d Generalized quantifiers and compact logic. Transactions of the American Mathematical Society, vol. 204 (1975), pp. 342-364.
Shelah, S. 1975e The monadic theory of order. Annals of Mathematics, vol. 102 (1975), pp. 379-419.
Shelah, S. 1975f Why there are many nonisomorphic models for unsuperstable theories. In: Proceedings of the International Congress of Mathematicians. Volume One, edited by James, R. D.. Canadian Mathematical Congress, 1975, pp. 259-264.
Shelah, S. 1976a Decomposing uncountable squares to countably many chains. Journal of Combinatorial Theory (A), vol. 21 (1976), pp. 110-114.
Shelah, S. 1976b Refuting Ehrenfeucht conjecture on rigid models. Israel Journal of Mathematics, vol. 25 (1976), pp. 273-286.
Shelah, S. 1977 A two-cardinal theorem and a combinatorial theorem. Proceedings of the American Mathematical Society, vol. 62 (1977), pp. 134-136.
Shelah, S. 1978a Classification Theory and the Number of Non-isomorphic Models. North-Holland Publishing Company, 1978, xvi+544 pp.
Shelah, S. 1978b End extensions and number of countable models. Journal of Symbolic Logic, vol. 43 (1978), pp. 550-562.
Shelah, S. 1978c Models with second order properties, I: Boolean algebras with no un-definable automorphisms. Annals of Mathematical Logic, vol. 14 (1978), pp. 57-72.
Shelah, S. 1978d Models with second order properties, II: Trees with no undefined branches. Annals of Mathematical Logic, vol. 14 (1978), pp. 73-87.
Shelah, S. 1978c Appendix to “Models with second order properties, II: Trees with no undefined branches”. Annals of Mathematical Logic, vol. 14 (1978), pp. 223 226.
Shelah, S. 1979a On successors of singular cardinals. In: Logic Colloquium ’78, edited by BofFa, M., van Dalen, D. and McAloon, K.. North-Holland Publishing Company, 1979, pp. 357-380.
Shelah, S. 1979b On uncountable Abelian groups. Israel Journal of Mathematics, vol. 32 (1979), pp. 311-330.
Shelah, S. 1981a Models with second order properties, III: Omitting types for L(Q). Archiv für Mathematische Logik und Grundlagenforschung, vol. 21 (1981), pp. 1-11.
Shelah, S. 1981b On the number of non-isomorphic models of cardinality λ L∞λ-equivalent to a fixed model. Notre Dame Journal of Formal Logic, vol. 22 (1981), pp. 5-10,
Shelah, S. 1982a Measure, Craig, L(aa), finite axiomatizability. Abstracts of Papers Presented to the American Mathematical Society, vol. 3 (1982), p. 130. Abstract.
Shelah, S. 1982b On the number of non-isomorphic models in L∞κ when κ is weakly compact. Notre Dame Journal of Formal Logic, vol. 23 (1982), pp. 21-26.
Shelah, S. 1982c Proper forcing. Springer-Verlag Lecture Notes in Mathematics, vol. 940, 1982, xxix+496 pp.
Shelah, S. 1982d The sprectrum problem, I: א∊-saturated models, the main gap. Israel Journal of Mathematics, vol. 43 (1982), pp. 324-356.
Shelah, S. 1982e The spectrum problem, II: Totally transcendental and infinite depth. Israel Journal of Mathematics, vol. 43 (1982), pp. 357-364.
Shelah, S. 1982f Why am I so happy? Abstracts of Papers Presented to the American Mathematical Society, vol. 3 (1982), p. 282. Abstract.
Shelah, S. 1983a A classification of generalized quantifiers. Manuscript, The Hebrew University of Jerusalem, 1983.
Shelah, S. 1983b Classification theory of non-elementary classes, I: The number of uncountable models of ψ ∈ Lω1ω. Part A. Israel Journal of Mathematics, vol. 46 (1983), pp. 212-240.
Shelah, S. 1983c Classification theory of non-elementary classes, I: The number of uncountable models of ψ ∈ Lω1ω. Part B. Israel Journal of Mathematics, vol. 46 (1983), pp. 241-273.
Shelah, S. 1983d Models with second order properties, IV: A general method and eliminating diamonds. Annals of Pure and Applied Logic, vol. 25 (1983), pp. 183-212.
Shelah, S. 1983e Results in math, logic, I. Abstracts of Papers Presented to the American Mathematical Society, vol. 4 (1983), p. 189. Abstract.
Shelah, S. 1984a On co-K-Souslin relations. Israel Journal of Mathematics, vol. 47 (1984), pp. 139-153.
Shelah, S. 1984b A pair of nonisomorphic ≡∞λ models of power λ for λ singular with λω = λ. Notre Dame Journal of Formal Logic, vol. 25 (1984), pp. 97-104.
Shelah, S. 198?a “L<ω; is not countably compact” is consistent. Manuscript, Hebrew University. In preparation.
Shelah, S. 198?b Monadic logic: Löwenheim numbers. Annals of Pure and Applied Logic. To appear.
Shelah, S. 198?c Classification theory for non-elementary classes, II: Abstract elementary classes. Manuscript, Hebrew University. In preparation.
Shelah, S. 198?d Monadic Logic: IIanf numbers. Annals of Pure and Applied Logic. To appear.
Shelah, S. 198?e Remarks on Abstract Model Theory. APAL. To appear.
See also: Baldwin, J. T. and Shelah, S. 1982; Devlin, K. J. and Shelah, S. 1978; Friedman, S. D. and Shelah, S. 1983; Giorgetta, D. and Shelah, S. 1984; Grossberg, R. and Shelah, S. 1983; Gurevich, Y. and Shelah, S. 1979; Gurevich, Y. and Shelah, S. 1981a; Gurevich, Y. and Shelah, S. 1981b; Gurevich, Y. and Shelah, S. 1981c; Gurevich, Y. and Shelah, S. 1982; Gurevich, Y. and Shelah, S. 1983a; Gurevich, Y. and Shelah, S. 1983b; Gurevich, Y. and Shelah, S. 1983c; Gurevich, Y., Magidor, M. and Shelah, S. 1983; Harrington, L. A. and Shelah, S. 1982; Harrington, L. A., Makkai, M. and Shelah, S. 198?; Hodges, W. and Shelah, S. 1981; Macintyre, A. J. and Shelah, S. 1976; Magidor, M. and Shelah, S. 1983; Magidor, M., Shelah, S. and Stavi, J. 1984; Makowsky, J. A. and Shelah, S. 1976; Makowsky, J. A. and Shelah, S. 1979a; Makowsky, J. A. and Shelah, S. 1979b; Makowsky, J. A. and Shelah, S. 1981; Makowsky, J. A. and Shelah, S. 1983; Makowsky, J. A. and Shelah, S. 198?a; Makowsky, J. A. and Shelah, S. 198?b; Makowsky, J. A., Shelah, S., and Stavi, J. 1976; Mekler, A. H. and Shelah, S. 1983; Mekler, A. H. and Shelah, S. 198?; Rubin, M. and Shelah, S. 1980; Rubin, M. and Shelah, S. 1983; Schmerl, J. H. and Shelah, S. 1972.
Shelah, S. and Kaufmann, M. J. 198?a The Hanf number of stationary logic I. Notre Dame Journal of Formal Logic. To appear.
Shelah, S. and Kaufmann, M. J. 198?b The Hanf number of stationary logic II. Notre Dame Journal of Formal Logic. To appear.
Shelah, S. and Steinhorn, C.I. 1982 On the non-axiomatizability of some logics by finitely many schemas. Abstracts of Papers Presented to the American Mathematical Society, vol. 3 (1982), p. 311. Abstract.
Shelah, S. and Steinhorn, C.I. 198? On the non-axiomatizability of some logics by finitely many schemas. Notre Dame Journal of Formal Logic. To appear.
Shelah, S. and Stern, J. 1978 The Hanf number of the first order theory of Banach spaces. Transactions of the American Mathematical Society, vol. 244 (1978), pp. 147 171.
Shelah, S. and Ziegler, M. 1979 Algebraically closed groups of large cardinality. Journal of Symbolic Logic, vol. 44 (1979), pp. 522-532.
Shoenfield, J. R. 1967 Mathematical Logic. Addison-Wesley, 1967, vii+344 pp.
Shoenfield, J. R. 1971 Unramified forcing. In: Axiomatic Set Theory, Part I, edited by Scott, D. S.. American Mathematical Society Proceedings of Symposia in Pure Mathematics, vol. 13 (1971), pp. 357-382.
Shore, R. A. 1977 α-recursion theory. In: Handbook of Mathematical Logic, edited by Barwise, K. J.. North-Holland Publishing Company, 1977, pp. 653-680.
Siefkes, D. 1968 Recursion theory and the theorem of Ramsey in one-place second order successor arithmetic. In: Contributions to Mathematical Logic, edited by Schmidt, H. A., Schütte, K. and Thiele, H.-J.. North-Holland Publishing Company, 1968, pp. 237-254.
Siefkes, D. 1970 Büchi's Monadic Second-order Successor Arithmetic. Spring-’ er-Verlag Lecture Notes in Mathematics, vol. 120, 1970, xii+130 pp.
See also: Bxichi, J. R. and Siefkes, D. 1973; Biichi, J. R. and Siefkes, D. 1983.
Sierpiński, W. 1950 Sur les types d'ordre des ensembles linéaires. Fundamenta Mathematicae, vol. 37 (1950), pp. 253-264.
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