Publications, H. Jerome Keisler

1. Theory of models with generalized atomic formulas, J. Symbolic Logic 25 (1960), pp. 1-26.

2. Ultraproducts and elementary classes, Ph. D. Thesis, Univ. of California, Berkeley, 1961, 45 pages.

3. On some results of Jonsson and Tarski concerning free algebras, Math. Scand. 9 (1961), pp. 102-106.

4. Ultraproducts and elementary classes, Indag. Math. 23 (1961), pp. 477-495.

5. Some applications of the theory of models to set theory, Proc. Int. Cong. of Logic, Methodology, and Philosophy of Science, Stanford 1962, pp. 80-85.

6. Model theories with truth values in a uniform space (with C.C.Chang), Bull. Amer. Math. Soc. 68 (1962), pp. 107-109.

7. An improved prenex normal form (with C.C.Chang), J. Symbolic Logic 27 (1962), pp. 317-326.

8. Applications of ultraproducts of pairs of cardinals to the theory of models (with C.C.Chang), Pacific J. Math. 12 (1962), pp. 835-845.

9. Limit ultrapowers, Trans. Amer. Math. Soc. 107 (1963), pp. 382-408.

10. A complete first-order logic with infinitary predicates, Fund. Math. 52 (1963), pp. 177-203.

11. Good ideals in fields of sets, Annals of Math. 79 (1964), pp. 338-359.

12. From accessible to inaccessible cardinals (with Alfred Tarski), Fund. Math. 53 (1964), pp. 225-308.

13. Ultraproducts and saturated models, Indag. Math. 26 (1964), pp. 179-186.

14. Complete theories of algebraically closed fields with distinguished subfields, Mich. Math. Journal 11 (1964), pp. 71-81.

15. On cardinalities of ultraproducts, Bull. Amer. Math. Soc. 70 (1964), pp. 644-647.

16. Unions of relational systems, Proc. Amer. Math. Soc. 13 (1964), pp. 540-545.

17. Ideals with prescribed degree of goodness, Annals of Math. 81 (1965), pp. 112-116.

18. Reduced products and Horn classes, Trans. Amer. Math. Soc. 117 (1965), pp. 307-328.

19. Limit ultraproducts, J. Symbolic Logic 30 (1965), pp. 212-234.

20. A survey of ultraproducts, Proc. Int. Cong.of Logic, Methodology, and Phil. of Sci., Amsterdam 1965, pp. 112-126.

21. Finite approximations of infinitely long formulas, Symposium on the Theory of Models, Amsterdam 1965, ed. by J. Addison, L. Henkin, and A. Tarski. pp. 158-169.

22. Some applications of infinitely long formulas, J. Symbolic Logic 30 (1965), pp. 339-349.

23. Universal homogeneous boolean algebras, Mich. Math. J. 13 (1966),pp. 129-132.

24. First-order properties of pairs of cardinals, Bull. Amer. Math. Soc. 72 (1966), pp. 141-144.

25. Continuous Model Theory (book) (with C.C.Chang), Annals of Math. Studies 58 (1966), xii+165 pages.

26. Some model-theoretic results for omega-logic, Israel J. Math. 4 (1966), pp. 249-261.

27. Ultraproducts which are not saturated, J. Symbolic Logic 32 (1967), pp. 23-46.

28. Ultraproducts of finite sets, J. Symbolic Logic 32 (1967), pp. 47-57.

29. On the number of homogeneous models of a given power (with Michael Morley), Israel J. Math. 5 (1967), pp. 73-78.

30. Elementary extensions of models of set theory (with Michael Morley), Israel J. Math. 6 (1968), pp. 49-65.

31. Models with orderings, Proc. of the Int. Cong. for Logic, Methodology and Phil. of Sci., Jerusalem 1968, pp. 35-62.

32. Infinite quantifiers and continuous games, Applications of Model Theory to Algebra, Analysis, and Probability, ed. by W. A. J. Luxemburg, 1968, pp. 228-264.

33. Formulas with linearly ordered quantifiers, The Syntax and Semantics of Infinitary Languages, ed. by J. Barwise, Springer-Verlag Lecture Notes in Math. 72 (1968), pp. 96-130.

34. Logic with the quantifier "there exist uncountably many", Ann. Math. Logic 1 (1970), pp. 1-93.

35. End extensions of models of set theory (with Jack Silver), Axiomatic Set Theory, Amer. Math. Soc. Proc. of Symp. in Pure Math. 13 (1971), pp. 177-187.

36. Model Theory for Infinitary Logic (book), North-Holland 1971, x+208 pages.

37. Model Theory, Proc. of the International Congress of Mathematicians (1970), Nice 1971, pp. 141-150.

38. On theories categorical in their own power, J. Symb. Logic 36 (1971), pp. 240-244.

39. Model Theory (book) (with C.C.Chang), North-Holland 1973, 554 pages. (Translated into Italian and Russian) (Second edition, 1977) (Third Edition, 650 pages, 1990) (Dover Edition, Dover Publications, 2012).

40. Elementary Calculus - An Approach Using Infinitesimals (experimental version), (book), Bogden and Quigley, 1971.

41. The diversity of quantifier prefixes (with Wilbur Walkoe), J. Symb. Logic 38 (1973), pp. 79-85.

42. Forcing and the omitting types theorem, M.A.A. Studies in Model Theory Vol. 8 (1973), pp. 96-133.

43. A result concerning cardinalities of ultraproducts (with Karel Prikry), J. Symb. Logic 39 (1974), pp. 43-48.

44. Monotone complete ordered fields, Victoria Symposium on Nonstandard Analysis (1974), Spinger Lecture Notes in Math. 369, pp. 113-115.

45. Models with tree structures, Tarski Symposium, Amer. Math. Soc. Proc. of Symp. in Pure Math. 25 (1974), pp. 331-348.

46. Constructions in model theory, Model Theory and its Applications, C.I.M.E., Rome, Italy 1975, pp. 56-108.

47. Six classes of theories, J. Australian Math. Soc. Ser. A, 25 (1976), pp. 257-266.

48. Elementary Calculus, An Approach Using Infinitesimals. (book), Prindle, Weber and Schmidt, 1976, xviii+940 pages. (Italian translation, 1982) (Second Edition 1986) (Online edition. 2000).

49. Foundations of Infinitesimal Calculus (book), Prindle, Weber and Schmidt, 1976, ix+214 pages. (Japanese translation, 1981).

50. Preface to second edition of Complete Theories by A. Robinson, North-Holland 1977.

51. The monotone class theorem in infinitary logic, Proc. Amer. Math. Soc. 64 (1977), pp. 129-134.

52. Hyperfinite model theory, Logic Colloquium 76, 1977, pp. 5-110.

53. Fundamentals of Model Theory, Handbook of Math. Logic, 1978, pp. 47-103.

54. The stability function of a theory, J. Symb. Logic 43 (1978), pp. 481-486.

55. L_A(F) (with Kim Bruce), J. Symb. Logic 44 (1979), pp. 15-28.

56. Collected Works of Abraham Robinson, editor, volume 1, Yale Univ. 1979.

57. An infinitesimal approach to stochastic analysis, Memoirs of the Amer. Math. Soc., No. 297 (1984), x + 184 pages.

58. The strength of nonstandard methods in arithmetic (with C. Ward Henson and Matt Kaufmann), J. Symb. Logic, 49 (1984), pp. 1039-1058.

59. Adapted probability distributions (with Douglas Hoover). Trans. Amer. Math. Soc., vol. 286 (1984), pp. 159-201.

60. Probability Quantifiers. Model Theoretic Languages, Springer-Verlag, pages 509-556 in Model Theoretic Logics, edited by J. Barwise and S. Feferman, 1985.

61. A price adjustment model with infinitesimal traders. In Models of Economic Dynamics, pp. 69-87, ed. by H. Sonnenschein, Springer-Verlag 1986.

62. A completeness proof for adapted probability logic. Annals of Pure and Applied Logic, vol. 31 (1986), pp. 61-70.

63. Hyperfinite models of adapted probability logic. Annals of Pure and Applied Logic, vol. 31 (1986), pp. 71-86.

64. On the strength of nonstandard analysis (with C. Ward Henson), J. Symb. Logic, vol. 51 (1986), pp. 377-386.

65. Measures and forking. Annals of Pure and Applied Logic 34 (1987), pp. 119-169.

66. Choosing elements in a saturated model. pp. 165-181 in "Classification Theory", ed. by J. Baldwin, Springer-Verlag Lecture Notes # 1292, (1987).

67. Infinitesimals in probability theory. Pp. 106-139 in Proceedings of the Symposium on nonstandard analysis, ed. by N. Cutland, Hull, 1988.

68. Descriptive set theory over hyperfinite sets (with Kenneth Kunen, Steven Leth, and Arnold Miller). J. Symb. Logic 54 (1989), pp. 1167-1180.

69. Meager sets in the hyperfinite time line (with Steven Leth). J. Symb. Logic, 56 (1991), pp. 71-103.

70. From discrete to continuous time. Annals of Pure and Applied Logic 52 (1991), pp. 99-141.

71. Making the hyperreal line both saturated and complete (with James Schmerl). Journal of Symbolic Logic 56 (1991), pp. 1016-1025.

72. A law of large numbers for fast price adjustment. Trans. Amer. Math. Soc., 332 (1992), pp. 1-51.

73. Game sentences and ultrapowers (with Renling Jin). Annals of Pure and Applied Logic 60 (1993), pp. 261-274.

74. The hyppereal line. In Real Numbers, Generalizations of the Reals, and Theories of Continua, ed. by P. Erlich, Kluwer Academic Publishers, pp. 207-237, 1994.

75. Approximate tatonnement processes. Economic Theory, vol. 5 (1995), 127-173.

76. Neocompact sets and stochastic Navier-Stokes equations (with Nigel Cutland). Pp. 31-54 in Stochastic Partial Differential Equations, London Mathematical Society Lecture Notes Series 216, ed. by A. Etheridge, Cambridge Univ. Press 1995.

77. A neometric survey. Pp. 233-250 in Developments in Nonstandard Analysis, ed. by N. Cutland et al, Longman 1995.

78. Long sequences in neocompact sets (with Sergio Fajardo). Pp. 251-260 in Developments in Nonstandard Analysis, ed. by N. Cutland et al, Longman 1995.

79. Getting to a competitive equilibrium. Econometica, vol. 64 (1996), pp. 29-49.

80. Neometric spaces (with Sergio Fajardo). Advances in Math. 118 (1996), pp. 134-175.

81. Existence theorems in probability theory (with Sergio Fajardo). Advances in Math. 120 (1996), pp. 191-257.

82. Mathematical Logic and Computability (with Joel Robbin et al). McGraw-Hill 1996, 484 pages with accompanying software.

83. Rich and Saturated Adapted Spaces. Advances in Math. 128 (1997), pp. 242-288.

84. Expressive Power of Unary Counters (with Michael Benedikt). Pp. 34-50 in Structures in Logic and Computer Science, edited by J. Mycielski et al, Lecture Notes in Computer Science 1261 (1997), Springer.

85. Stochastic Differential Equations with Extra Properties. Pp. 259-277 in Nonstandard Analysis, Theory and Applications, edited by L. Arkeryd et al, NATO ASI Series C Vol. 493, Kluwer 1997.

86. Quantifier elimination for neocompact sets. J. Symbolic Logic, 63 (1998), pp. 1442-1472.

87. Randomizing a model. Advances in Math. 143 (1999), pp. 124-158.

88. Maharam spectra of Loeb spaces (with Renling Jin). J. Symbolic Logic 65 (2000), pp. 550-566.

89. Definability over linear constraints (with Michael Benedikt). In Computer Science Logic, Fischbachau 2000, pp. 217-231. Lecture Notes in Computer Science No. 1862, Springer-Verlag 2000.

90. Categoricity without equality (with Arnold Miller). Fund. Math. 170 (2001), pp. 87-106.

91. Epistemic Conditions for Iterated Admissibility (with Adam Brandenburger), Extended abstract in Theoretical Aspects of Rationality in Knowledge: Proc.of Eighth Congress, ed. by J. van Benthem, Morgan Kaufmann 2001, pp. 31-37.

92. Loeb measures and Borel algebras (with Yeneng Sun). Pp. 111-118 in Reuniting the Antipodes---Constructive and Nonstandard Views of the Continuum. Proceedings of the Symposion in San Servolo/Venice, Italy, U. Berger, H. Osswald, and P. Schuster, editors, Kluwer 2002.

93. Model theory for algebraists. In The Concise Handbook of Algebra, ed. by A. V. Mikhalev and G. Pilz, Kluwer 2002, pp. 523-525.

94. Abelian Groups with Layered Tiles and the Sumset Phenomenon (with Renling Jin), Trans. Amer. Math. Soc. 355 (2002), pp. 79-97.

95. Model Theory of Stochastic Processes (with Sergio Fajardo) (book). Lecture Notes in Logic, Association for Symbolic Logic (2002), xii+136 pages..

96. Definability with a Predicate for a Semi-Linear Set (with Michael Benedikt), J. Symb. Logic 68 (2003), pp. 319-351.

97. A Metric on Probabilities, and Products of Loeb Spaces (with Yeneng Sun). J. London Math. Society 69 (2004), pp. 258-272.

98. Barwise: Infinitary Logic and Admissible Sets (with Julia Knight). Bulletin of Symbolic Logic 10 (2004), pp 4-26.

99. Shrinking Games and Local Formulas (with Wafik Lotfallah), Annals of Pure and Applied Logic 128 (2004), pp. 215-225.

100. An Impossibility Theorem on Beliefs in Games (with Adam Brandenburger), Studia Logica 84 (2006), pp. 211-240. Also Chapter 1 in "The Language of Game Theory", Adam Brandenburger, World Scientific 2014.

101. Global attractors for 3-dimensional stochastic Navier-Stokes equations (with Nigel Cutland), J. Dynamics and Differential Equations 16 (2004), 205-266.

102. Attractors and Neo-attractors for 3D Stochastic Navier--Stokes Equations (with Nigel Cutland), Journal of Stochastics and Dynamics 5 (2005), pp. 487-533.

103. First Order Quantifiers in Monadic Second Order Logic (with Wafik Lotfallah). Journal of Symbolic Logic 69 (2004), pp. 118-136.

104. Neoclosed Forcing (with Sergio Fajardo), Pp. 45-79 in "Nonstandard Methods and Applications in Mathematics", Lecture Notes in Logic 25 (2006).

105. A Local Normal Form Theorem for Infinitary Logic with Unary Quantifiers (with Wafik Lotfallah). Mathematical Logic Quarterly 51 (2005), pp. 137-144.

106. The Strength of Nonstandard Analysis. In "The Strength of Nonstandard Analysis", edited by I. van den Berg and V. Neves, pp. 3-26 (2007).

107. Nonstandard Arithmetic and Reverse Mathematics. Bulletin of Symbolic Logic.12 (2006), pp. 100-125.

108. Admissibility in Games (with Adam Brandenburger and Amanda Friedenburg). Econometrica 76 (2008), 307-352. Also Chapter 7 in "The Language of Game Theory", Adam Brandenburger, World Scientific 2014.

109. Quantifiers in Limits. In "Andrej Mostowski and Foundational Studies", ed. by A. Ehrenfeucht et. al., IOS Press, Amsterdam (2008), pp. 151-170..

110. Foundations of Infinitesimal Calculus (book), Online edition, 2007. ix+203 pages.

111. Almost Everywhere Elimination of Probability Quantifiers (with Wafik Lotfallah). Journal of Symbolic Logic 74 (2009), pp. 1121-1142.

112. Randomizations of Models as Metric Structures (with Itai Ben Yaacov). Confluentes Mathematici 1 (2009), pp. 197-223.

113. Why Saturated Probability Spaces are Necessary (with Yeneng Sun). Advances in Mathematics 221 (2009), pp. 1584-1607.

114. The Ultraproduct Construction. In "Ultrafilters Across Mathematics", ed. by V. Bergelson et. al., Contemporary Mathematics 530 (2010), pp. 163-179, Amer. Math. Soc.

115. Nonstandard Analysis and Recursive Comprehension. Annals of Pure and Applied Logic 161 (2010) pp. 1047-1062.

116. Rank Hierarchies for Generalized Quantifiers (with Wafik Lotfallah). Journal of Logic and Computation 21 (2011), pp. 287-306.

117. Fixed Points in Epistemic Game Theory (with Adam Brandenburger and Amanda Friedenburg). In "Mathematical Foundations of Information Flow", Proceedings of 2008 Clifford Lectures, AMS Proc. of Symposia in Applied Mathematics, (2012), pp.49-60.

118. Craig Interpolation for Networks of Sentences (with Jeffrey M. Keisler). Annals of Pure and Applied Logic 163 (2012), pp. 1322-1344.

119. Iterated Dominance Revisited (with Amanda Friedenburg). Economic Theory 72 (2021), 377-421.

120 Common Assumption of Rationality (with Byung Soo Lee). To appear, Journal of Mathematical Economics, 2023.

121. Fiber Products of Measures and Quantum Foundations (with Adam Brandenburger). In Logic & Algebraic Structures in Quantum Computing & Information, edited by Jennifer Chubb, Ali Eskandarian, and Valentina Harizanov, in Lecture Notes in Logic, Association for Symbolic Logic, Cambridge University Press, 2016.

122. Observing, Reporting, and Deciding in Networks of Sentences (with Jeffrey M. Keisler). Annals of Pure and Applied Logic 165 (2014), pp. 812-836.

123. A Canonical Hidden-Variable Space (with Adam Branburger). To appear, Annals of Pure and Applied Logic, and available online.

124. Use of a Canonical Hidden Variable Space in Quantum Mechanics (with Adam Brandenburger). In Computation, Logic, Games, and Quantum Foundations: The Many Facets of Samson Abramsky, ed. by Bob Coecke, Luk Ong, and Prakash Panangaden, Lecture Notes in Computer Science 7860, Springer 2013, pp. 1-6.

125. Definable Closure in Randomizations (with Uri Andrews and Isaac Goldbring). Annals of Pure and Applied Logic 166 (2015), pp. 325-341.

126. Separable Models of Randomizations (with Uri Andrews). Journal of Symbolic Logic 80 (2015), 1149-1181.

127. Independence in Randomizations. (with Uri Andrews and Isaac Goldbring). Jounal of Mathematical Logic, Vol. 19 (2019), no. 01. arXiv:1703.10913, 2017.

128. Randomizations of Scattered Sentences. Pp. 189-218 in "Beyond First Order Model Theory", edited by Jose Iovino, CRC Press.

129. Review of Three Papers by Malliaris and Shelah. Bulletin of Symbolic Logic 23 (2017), pp. 117-121.

130. Scattered Sentences Have Few Separable Randomizations (with Uri Andrews, Isaac Goldbring, Sherwood Hachtman, and David Marker). Archive for Mathematical Logic. First Online: 03 February 2020. arXiv:1704.04981, 2017.

131. On the Converse Law of Large Numbers (with Yeneng Sun). Illinois Journal of Mathematics 24 (2020), pp. 199-225.

132. Model Theory for Real-valued Structures. To appear in "Beyond First Order Model Theory, Volume II", ed. by Jose Iovino, Chapman & Hall (2023). arXiv:2005.11851, 2020. arXiv:2005.11851, 2020.

133. Cooperative Games on Infinite Trees (with Adam Brandenburger and Paula Miret).

134. Continuous Sentences Preserved Under Reduced Products (with Isaac Goldbring). Journal of Symbolic Logic, vo.. 87 (2022), 649-681. arXiv:1905.10673, 2019.

135. Using Ultrapowers to Compare Continuous Structures. To apear, Annals of Pure and Appled Logic. arXiv:2206.06969, 2022.

136. The relationship between strong belief and assumption (with Adam brandenburge and Amanda Friedenberg). Open access article. Synthese, vol. 201, issue 5, May 2023.