Publications of T. Jech

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1 Publications of T. Jech 1. (with B. Balcar), Modeli teorii mnoжestv obrazovannye soverxennym otnoxeniem, (Models of set theory given by perfect relations), Časopis pro pěstování matematiky 90 (1965), , MR 35, # On ordering of cardinalities, Bulletin de l Académie Polonaise des Sciences 14 (1966), , MR 34, # (with A. Sochor), On θ-model of the set theory, Bulletin de l Académie Polonaise des Sciences 14 (1966), , MR 34, # (with A. Sochor), Applications of the θ-model, Bulletin de l Académie Polonaise des Sciences 14 (1966), , MR 37, # Interdependence of weakened forms of the axiom of choice, Commentationes Mathematicae Universitatis Carolinae 7 (1966), , MR 34, # On cardinals and their successors, Bulletin de l Académie Polonaise des Sciences 14 (1966), , MR 37, # Non-provability of Souslin s hypothesis, Commentationes Mathematicae Universitatis Carolinae 8 (1967), , MR 35, # Eine Bemerkung zum Auswahlaxiom, Časopis pro pěstování matematiky 93 (1968), 30 31, MR 38, # ω 1 can be measurable, Israel Journal of Mathematics 6 (1968), , MR 39, # Isomorphism types of trees, Notices Amer. Math. Society 17 (1970), On models for set theory without AC, Axiomatic Set Theory, Proceedings of Symposia in Pure Mathematics XIII, Part I (D. Scott, ed.), American Mathematical Society, Providence, RI, 1971, pp , MR 43, # Trees, Journal of Symbolic Logic 36 (1971), 1 14, MR 44, # The closed unbounded filter over P κ (λ), Notices Amer. Math. Society 18 (1971), Lectures in set theory with particular emphasis on the method of forcing, Lecture Notes in Mathematics vol. 217, Springer-Verlag, Berlin, 1971, MR 48, # (with W. Powell), Standard models of set theory with predication, Bulletin Amer. Math. Society 77 (1971), , MR 43, # Two remarks on elementary embeddings of the universe, Pacific J. Math. 39 (1971), , MR 46, # Some species of trees, Notices Amer. Math. Society 19 (1972), A A propos d algèbres de Boole rigides et minimales, C.R. Acad. Sc. Paris 274 (1972), , MR 44, # Automorphisms of ω 1 -trees, Transactions Amer. Math. Society 173 (1972), 57 70, MR 50, # Some combinatorial problems concerning uncountable cardinals, Annals Math. Logic 5 (1973), , MR 48, # The Axiom of Choice, Studies in Logic and the Foundations of Mathematics vol. 75, North-Holland Publ. Co., Amsterdam, 1973, MR 53, #139.

2 22. (with U. Felgner), Variants of the axiom of choice in set theory with atoms, Fundamenta Mathematicae 79 (1973), 79 85, MR 47, # Properties of the gimel function and a classification of singular cardinals, Fundamenta Mathematicae 81 (1973), 57 64, MR 52, # Teoria mnoжestv i metod forsinga, Russian translation of [14], Mir, Moscow, 1973, MR 49, # On a problem of Rubin and Rubin, Notices Amer. Math. Society 21 (1974), A A descending sequence of models of HOD sets, Notices Amer. Math. Society 21 (1974), A Simple complete Boolean algebras, Israel Journal of Mathematics 18 (1974), 1 10, MR 51, # Forcing with trees and ordinal definability, Annals Math. Logic 7 (1974), , MR 51, # (editor), Axiomatic Set Theory, Proc. Symp. of Pure Math. vol. XIII, Part II, Amer. Mathematical Society, Providence, RI, Almost disjoint families of stationary sets, Notices Amer. Math. Society 22 (1975), A (with L. Harrington), On Σ 1 well-orderings of the universe, Journal of Symbolic Logic 41 (1976), , MR 53, # An infinite game played with stationary sets, Notices Amer. Math. Society 23 (1976), A A note on countably generated complete Boolean algebras, Proceedings Amer. Math. Society 56 (1976), , MR 53, # (with K. Prikry), On ideals of sets and the power set operation, Bulletin Amer. Math. Society 82 (1976), , MR 58, # A Boolean algebraic game, Notices Amer. Math. Society 24 (1977), A Precipitous ideals, Logic Colloquium 76, (R. Gandy and M. Hyland, eds.), North-Holland Publ. Co., Amsterdam, 1977, pp , MR 58, # About the axiom of choice, Handbook of Mathematical Logic, (J. Barwise, ed.), North-Holland Publ. Co., Amsterdam, 1977, pp , MR 58, # (with K. Hrbacek), Introduction to Set Theory, M. Dekker, Inc., New York, 1978, MR 58, # (with F. Galvin and M. Magidor), An ideal game, Journal of Symbolic Logic 43 (1978), , MR 58, # Set Theory, Academic Press, New York, 1978, (Review: Bulletin Amer. Math. Society vol. 3 (1980), ) MR 80a: Set Theory, Chinese edition of [40], Beijing. 42. A game theoretic property of Boolean algebras, Logic Colloquium 77, (A. Macintyre et al., eds.), North-Holland Publ. Co., Amsterdam, 1978, pp , MR 80c: (with K. Prikry), Ideals over uncountable sets: Application of almost disjoint functions and generic ultrapowers, Memoirs Amer. Math. Society vol. 18, no. 214, American Mathematical Society, Providence, RI, 1979, MR 80f:03059.

3 44. (with K. Prikry), On projections of finitely additive measures, Proceedings Amer. Math. Society 74 (1979), , MR 80f: (with M. Magidor, W. Mitchell and K. Prikry), Precipitous ideals, Journal of Symbolic Logic 45 (1980), 1 8, MR 81h: On a problem of L. Nachbin, Proceedings Amer. Math. Society 79 (1980), , MR 81d: On the number of generators of an ideal, Notre Dame J. Formal Logic 22 (1981), , MR 83i: A maximal definable σ-ideal over ω 1, Israel Journal of Mathematics 39 (1981), , MR 84a: The brave new world of determinacy, Review of Descriptive Set Theory by Y. N. Moschovakis, Bulletin Amer. Math. Society 5 (1981), On hereditarily countable sets, Jour. Symbolic Logic 47 (1982), 43 47, MR 83e: A note on countable Boolean algebras, Algebra Universalis 14 (1982), , MR 83a: The ranking of incomplete tournaments: a mathematician s guide to popular sports, American Math. Monthly 90 (1983), , MR 85i: (with W. Mitchell), Some examples of precipitous ideals, Annals of Pure and Applied Logic 24 (1983), , MR 85k: Some properties of κ-complete ideals defined in terms of infinite games, Annals of Pure and Applied Logic 26 (1984), 31 45, MR 85h: More game-theoretic properties of Boolean algebras, Annals of Pure and Applied Logic 26 (1984), 11 29, MR 85j: (with Karel Prikry), Cofinality of the partial ordering of functions from ω 1 into ω under eventual domination, Math. Proc. Cambridge Phil. Soc. 95 (1984), 25 32, MR 85b: Stationary subsets of inaccessible cardinals, Axiomatic Set Theory, Contemporary Mathematics, vol. 31 (J. Baumgartner, ed.), American Mathematical Society, Providence, RI, 1984, pp , MR 86c: (with Karel Hrbacek), Introduction to Set Theory, 2nd edition, Marcel Dekker Inc., New York, 1984, MR 85m: Introduction to Set Theory, Chinese edition of [58], Beijing. 60. Abstract theory of abelian operator algebras: an application of forcing, Transactions Amer. Math. Society 289 (1985), , MR 87f: (with H. Woodin), Saturation of the closed unbounded filter on the set of regular cardinals, Transactions Amer. Math. Society 292 (1985), , MR 87d: A theorem on P κ (λ), J. Math. Soc. Japan 38 (1986), , MR 87f: (with Andreas Blass), On the Egoroff property of pointwise convergent sequences of functions, Proceedings Amer. Math. Society 98 (1986), , MR 87i: Multiple Forcing, Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 1986, (Review: Bulletin Amer. Math. Society vol. 20 (1989), ) MR 89h:03001.

4 65. A hierarchy of filters on regular uncountable cardinals, Journal of Symbolic Logic 52 (1987), , MR 88e: First order theory of complete Stonean algebras (Boolean-valued real and complex numbers), Canad. Math. Bulletin 30 (1987), , MR 89h: A quantitative theory of preferences: some results on transition functions, Social Choice and Welfare 6 (1989), , MR 91e: Distributive laws, Chapter 8, Handbook of Boolean Algebra, (J. D. Monk, ed.), NorthHolland Publ. Co., Amsterdam, 1989, pp , MR 90k: Boolean-valued models, Chapter 27, Handbook of Boolean Algebra, (J. D. Monk, ed.), North-Holland Publ. Co., Amsterdam, 1989, pp , MR 90k: (with Qi Feng), Local clubs, reflection, and preserving stationary sets, Proceedings London Math. Society 58 (1989), , MR 90a: Positive Σ operations on ordinals and normal filters on greatly Mahlo cardinals, Journal of Symbolic Logic 54 (1989), , MR 90a: A remark on a principle of Brézis and Browder, Applied Math. Letters 2 (1989), (with S. Shelah), A note on canonical functions, Israel Journal of Mathematics 68 (1989), , MR 90m: Boolean-linear spaces, Advances in Mathematics 81 (1990), , MR 91d: (with S. Shelah), Full reflection of stationary sets below ℵ ω, Journal of Symbolic Logic 55 (1990), , MR 91i: Local topology and a spectral theorem, Operator Theory: Advances and Applications 48 (1990), , MR 93m: On the cofinality of countable products of cardinal numbers, A tribute to Paul Erdős, (A. Baker, B. Bollobás and A. Hajnal, eds.), Cambridge University Press, 1990, pp , MR 92m: (with Marcia Groszek), Generalized iteration of forcing, Transactions Amer. Math. Society 324 (1991), 1 26, MR 91f: The infinite, Jahrbuch 1990 der Kurt-Gödel-Gesellschaft, Wien, 1991, pp , MR 93h: (with S. Shelah), On a conjecture of Tarski on products of cardinals, Proceedings Amer. Math. Society 112 (1991), , MR 91j: (with S. Shelah), A partition theorem for pairs of finite sets, Journal Amer. Math. Society 4 (1991), , MR 93a: The logarithmic distribution of leading digits and finitely additive measures, Discrete Mathematics 108 (1992), 53 57, MR 93i: Singular cardinal problem: Shelah s theorem on 2 ℵ ω, Bulletin of the London Math. Society 24 (1992), , MR 93a: (with S. Shelah), Full reflection of stationary sets at regular cardinals, American Journal of Mathematics 115 (1993), , MR 94m: A variation on a theorem of Galvin and Hajnal, Bulletin of the London Math. Society 25 (1993), , MR 94h:03089.

5 86. On Gödel s Second Incompleteness Theorem, Proceedings Amer. Math. Society 121 (1994), , MR 94g: (with J. Witzany), Full reflection at a measurable cardinal, J. Symbolic Logic 59 (1994), , MR 96c: OTTER experiments in a system of combinatory logic, J. Automated Reasoning 14 (1995), , MR 96c: Singular cardinals and the pcf theory, Bulletin of Symbolic Logic 1 (1995), , MR 97d: (with S. Shelah), Possible pcf algebras, J. Symbolic Logic 61 (1996), , MR 97g: (with S. Shelah), A complete Boolean algebra that has no proper atomless complete subalgebra, Journal of Algebra 182 (1996), , MR 97j: (with S. Shelah), On countably closed complete Boolean algebras, Journal of Symbolic Logic 61 (1996), , MR 98h: (with R. Dougherty), Left-distributive embedding algebras, Electronic Research Announcements of the American Math. Society 3 (1997), 28-37, MR 98b: Large ordinals, Advances in Mathematics 125 (1997), , MR 98g: (with R. Dougherty), Finite left-distributive algebras and embedding algebras, Advances in Mathematics 130 (1997), , MR 99f: (with B. Balcar and J. Zapletal), Semi-Cohen Boolean algebras, Annals of Pure and Applied Logic 87 (1997), , MR 99a: Set Theory, 2nd edition, Springer-Verlag, Heidelberg, 1997, MR 99b: (with B. Balcar and W. Glowczynski), The sequential topology on complete Boolean algebras, Fundamenta Mathematicae 155 (1998), 59 78, MR 99b: (with Q. Feng), Projective stationary sets and a strong reflection principle, Journal of the London Math. Society 58 (1998), , MR 2000b: (with Karel Hrbacek), Introduction to Set Theory, 3rd edition, Marcel Dekker Inc., New York, 1999, MR 01c: Some results on combinators in the system TRC, Journal of Symbolic Logic 64 (1999), , MR 03a: The infinite, translation of [79] into Korean, Historia Math 12 (1999), (with S. Shelah), On reflection of stationary sets in P κ λ, Transactions of the American Math. Society 352 (2000), , MR 00j: (with S. Shelah), Simple complete Boolean algebras, Proceedings of the American Math. Society 129 (2001), , MR 01e: Set Theory, URL= The Stanford Encyclopedia of Philosophy, (Summer 2002 Edition, E. Zalta, ed.) Set Theory, The Third Millennium Edition, Springer-VerLag, Heidelberg, 2002, MR 2004g: (with B. Balcar and T. Pazák), Complete ccc Boolean algebras, the order sequential topology, and a problem of von Neumann, Bulletin of the London Math. Society 37 (2005), El infinito, translation of [79] into Spanish, La Gaceta de la RSME 8 (2005),

6 109. (with B. Balcar), Weak distributivity, a problem of von Neumann and the mystery of measurability, Bulletin Symb. Logic 12 (2006), Set Theory, Chinese edition of [106], Beijing, (with Q. Feng and J. Zapletal), On the structure of stationary sets, Science in China, Ser. A 50 (2007), The Axiom of Choice, Reprint of [21], Dover Publications, New York, (with B. Balcar), Contributions to the theory of weakly distributive complete Boolean algebras, Andrzej Mostowski and Foundational Studies, (A. Ehrenfeucht, V. W. Marek and M. Srebrny, eds.), IOS Press, Amsterdam, 2008, pp Algebraic characterizations of measure algebras, Proceedings of the American Mathematical Society 136 (2008), WHAT IS... Forcing?, Notices of the American Mathematical Society 55 (2008), Stationary sets, Handbook of Set Theory, (M. Foreman, A. Kanamori and M. Magidor, eds.), Springer, 2010, pp Translation of [100] into Farsi Measures on Boolean algebras, Fundamenta Math. 239 (2017), Convergence and submeasures in Boolean algebras, to appear.

A Course in Model Theory

A Course in Model Theory Author address: Rami Grossberg 1 DEPARTMENT OF MATHEMATICAL SCIENCES, CARNEGIE MELLON UNI- VERSITY, PITTSBURGH, PA 15213 E-mail address: rami@cmu.edu 1 This preliminary draft is