Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 10
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Ivanov, A. 2010. A countably categorical theory which is not G-compact. Siberian Advances in Mathematics, Vol. 20, Issue. 2, p. 75.

    Casanovas, Enrique and Peláez, Rodrigo 2005. |T |+-resplendent models and the Lascar group. MLQ, Vol. 51, Issue. 6, p. 626.

    Warner, Steve 2004. The cofinality of the saturated uncountable random graph. Archive for Mathematical Logic, Vol. 43, Issue. 5, p. 665.

    CASANOVAS, E. LASCAR, D. PILLAY, A. and ZIEGLER, M. 2001. GALOIS GROUPS OF FIRST ORDER THEORIES. Journal of Mathematical Logic, Vol. 01, Issue. 02, p. 305.

    Ivanov, Alexandre A. and Macpherson, Dugald 1999. Strongly determined types. Annals of Pure and Applied Logic, Vol. 99, Issue. 1-3, p. 197.

    Kim, Byunghan and Pillay, Anand 1997. Simple theories. Annals of Pure and Applied Logic, Vol. 88, Issue. 2-3, p. 149.

    Hodges, Wilfrid Hodkinson, I.M. and Macpherson, Dugald 1990. Omega-categoricity, relative categoricity and coordinatisation. Annals of Pure and Applied Logic, Vol. 46, Issue. 2, p. 169.

    Hodges, Wilfrid 1989. Logic Colloquium'87, Proceedings of the Colloquium held in Granada.

    Makkai, M. 1985. Methods in Mathematical Logic.

    Lascar, Daniel 1984. Logic Colloquium '82.


On the category of models of a complete theory

  • Daniel Lascar (a1) (a2)
  • DOI:
  • Published online: 01 March 2014

Let T be a countable complete theory and C(T) the category whose objects are the models of T and morphisms are the elementary maps. The main object of this paper will be the study of C(T). The idea that a better understanding of the category may give us model theoretic information about T is quite natural: The (semi) group of automorphisms (endomorphisms) of a given structure is often a powerful tool for studying this structure. But certainly, one of the very first questions to be answered is: “to what extent does this category C(T) determine T?”

There is some obvious limitation: for example let T0 be the theory of infinite sets (in a language containing only =) and T1 the theory, in the language ( =, U(ν0),f(ν0)) stating that:

(1) U is infinite.

(2)f is a bijective map from U onto its complement.

It is quite easy to see that C(T0) is equivalent to C(T1). But, in this case, T0 and T1 can be “interpreted” each in the other. To make this notion of interpretation precise, we shall associate with each theory T a category, loosely denoted by T, defined as follows:

(1) The objects are the formulas in the given language.

(2) The morphisms from into are the formulas such that

(i.e. f defines a map from ϕ into ϕ; two morphisms defining the same map in all models of T should be identified).

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *