Introductory texts

• Doets, K., 1996, Basic Model Theory, Stanford: CSLI Publications. (Scholar)
• Hodges, W., 1997, A Shorter Model Theory, Cambridge: Cambridge University Press. (Scholar)
• Manzano, M., 1999, Model Theory, Oxford: Oxford University Press. (Scholar)
• Rothmaler, P., 2000, Introduction to Model Theory, Amsterdam: Gordon and Breach. (Scholar)

Model-theoretic definition

• Frege, G., 1906, “Grundlagen der Geometrie”, Jahresbericht der deutschen Mathematikervereinigung, 15: 293–309, 377–403, 423–430. (Scholar)
• Gergonne, J., 1818, “Essai sur la théorie de la définition”, Annales de Mathématiques Pures et Appliquées, 9: 1–35. (Scholar)
• Hilbert, D., 1899, Grundlagen der Geometrie, Leipzig: Teubner. (Scholar)
• Hodges, W., 2008, “Tarski’s theory of definition”, in Patterson, D. New Essays on Tarski and Philosophy, Oxford: Oxford University Press, pp. 94–132. (Scholar)
• Lascar, D., 1998, “Perspective historique sur les rapports entre la théorie des modèles et l’algèbre”, Revue d’histoire des mathématiques, 4: 237–260. (Scholar)
• Mancosu, P., Zach, R. and Badesa, C., 2009, “The development of mathematical logic from Russell to Tarski”, in L. Haaparanta (ed.), The Development of Modern Logic, Oxford: Oxford University Press, pp. 318–470. (Scholar)
• Pasch, M., 1882, Vorlesungen über Neuere Geometrie, Berlin: Springer-Verlag. (Scholar)
• Robinson, A., 1952, “On the application of symbolic logic to algebra”, Proceedings of the International Congress of Mathematicians (Cambridge, MA, 1950, Volume 1), Providence, RI: American Mathematical Society, pp. 686–694. (Scholar)
• Suppes, P., 1957, “Theory of definition” in Introduction to Logic (Chapter 8), Princeton, NJ: Van Nostrand. (Scholar)
• Tarski, A., 1954, “Contributions to the theory of models, I”, Indagationes Mathematicae, 16: 572–581. (Scholar)

Model-theoretic consequence

• Blanchette, P., 1996, “Frege and Hilbert on consistency”, The Journal of Philosophy, 93: 317–336. (Scholar)
• –––, 2012, Frege’s Conception of Logic, New York: Oxford University Press. (Scholar)
• Boole, G., 1847, The Mathematical Analysis of Logic, Cambridge: Macmillan, Barclay and Macmillan. (Scholar)
• Etchemendy, J., 1990, The Concept of Logical Consequence, Cambridge, MA: Harvard University Press. (Scholar)
• Frege, G., 1971, On the Foundations of Geometry, and Formal Theories of Arithmetic, E. Kluge (trans.), New Haven: Yale University Press. (Scholar)
• Gómez-Torrente, M., 1996, “Tarski on logical consequence”, Notre Dame Journal of Formal Logic, 37: 125–151. (Scholar)
• Hodges, W. 2004, “The importance and neglect of conceptual analysis: Hilbert-Ackermann iii.3”, in V. Hendricks et al. (eds.), First-Order Logic Revisited, Berlin: Logos, pp. 129–153. (Scholar)
• –––, 2018, “Two early Arabic applications of model-theoretic consequence”, Logica Universalis, 12: 37–54. (Scholar)
• Kreisel, G., 1969, “Informal rigour and completeness proofs”, in J. Hintikka (ed.), The Philosophy of Mathematics, London: Oxford University Press, pp. 78–94. (Scholar)
• Tarski, A., 1983, “On the concept of logical consequence”, translated in A. Tarski, Logic, Semantics, Metamathematics, J. Corcoran (ed.), Indianapolis: Hackett, pp. 409–420. (Scholar)
• van Benthem, J., 1991 [1983], The Logic of Time: A Model-Theoretic Investigation into the Varieties of Temporal Ontology and Temporal Discourse, Dordrecht: Reidel, 1983; second edition, Springer, 1991. (Scholar)

Expressive strength

• Cutland, N., 2009, Nonstandard Analysis and its Applications, Cambridge: Cambridge University Press. (Scholar)
• Ebbinghaus, H.-D., and Flum, J., 1999, Finite Model Theory, Berlin: Springer-Verlag. (Scholar)
• Ebbinghaus, H.-D., Flum, J. and Thomas, W., 1984, Mathematical Logic, New York: Springer-Verlag. (Scholar)
• Fleuriot, J., 2001, A Combination of Geometry Theorem Proving and Nonstandard Analysis, with Application to Newton’s Principia, New York: Springer-Verlag. (Scholar)
• Immerman, N., 1999, Descriptive Complexity, New York: Springer-Verlag. (Scholar)
• Libkin, L., 2004, Elements of Finite Model Theory, Berlin: Springer-Verlag. (Scholar)
• Lindström, P., 1969, “On extensions of elementary logic”, Theoria, 35:1–11. (Scholar)
• Loeb, P. and Wolff, M. (eds.), 2000, Nonstandard Analysis for the Working Mathematician, Dordrecht: Kluwer. (Scholar)
• Robinson, A., 1967, “The metaphysics of the calculus”, in Problems in the Philosophy of Mathematics, I. Lakatos (ed.), Amsterdam : North-Holland, pp. 28–40. (Scholar)

Models and modelling

• Allwein, G. and Barwise, J. (eds.), 1996, Logical Reasoning with Diagrams, New York: Oxford University Press. (Scholar)
• Börger, E. and Stärk, R., 2003, Abstract State Machines: A Method for High-Level System Design and Analysis, Berlin: Springer-Verlag. (Scholar)
• Fowler, M., 2000, UML Distilled, Boston: Addison-Wesley. (Scholar)
• Garnham, A., 2001, Mental Models and the Interpretation of Anaphora, Philadelphia: Taylor and Francis. (Scholar)
• Gentner, D. and Stevens, A. (eds.), 1983, Mental Models, Hillsdale, NJ: Lawrence Erlbaum. (Scholar)
• Gurevich, Yuri, 1993, “Evolving Algebras: An Attempt to Discover Semantics”, in E. Börger (ed.), Specification and Validation Methods, pp. 9–36, Oxford: Oxford University Press. (Scholar)
• Hammer, E. and Danner, N., 1996, “Towards a Model Theory of Venn Diagrams”, in Allwein and Barwise (eds.) 1996, pp. 109–128. (Scholar)
• Johnson-Laird, P., 1983, Mental Models: Towards a cognitive science of language, inference, and consciousness, Cambridge: Cambridge University Press. (Scholar)
• Meijers, A. (ed.), 2009, Philosophy of Technology and Engineering Sciences, Amsterdam: Elsevier; see chapters W. Hodges, “Functional modelling and mathematical models”; R. Müller, “The notion of a model, theories of models and history”; and N. Nersessian, “Model based reasoning in interdisciplinary engineering”. (Scholar)
• Moktefi, A. and Shin, S.-J. (eds.), 2013, Visual Reasoning with Diagrams, Basel: Birkhäuser. (Scholar)
• Morgan, M. S. and Morrison, M. (eds.), 1999, Models as Mediators, Cambridge: Cambridge University Press. (Scholar)
• Pullum, G. K. and Scholz, B. C., 2001, “On the distinction between model-theoretic and generative-enumerative syntactic frameworks”, in Logical Aspects of Computational Linguistics (Lecture Notes in Computer Science: Volume 2099), P. De Groote et al. (eds.), Berlin: Springer-Verlag, pp. 17–43. (Scholar)
• Stenning, K., 2002, Seeing Reason, Oxford: Oxford University Press. (Scholar)
• Suppes, P., 1969, Studies in the Methodology and Foundations of Science, Dordrecht: Reidel. (Scholar)

Philosophy of model theory

• Baldwin, J., 2018, Model Theory and the Philosophy of Mathematical Practice: Formalization without Foundationalism, Cambridge: Cambridge University Press. (Scholar)
• Button, T. and Walsh, S., 2018, Philosophy and Model Theory, Oxford: Oxford University Press. (Scholar)