Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-09T07:33:13.640Z Has data issue: false hasContentIssue false

Fondements de la logique positive

Published online by Cambridge University Press:  12 March 2014

Itaï Ben Yaacov
Affiliation:
Université De Lyon, Université De Lyon 1, Institut Camille Jordan CNRS, UMR 5208, 43 Boulevard Du 11 Novembre 1918, 69622 Villeurbanne-Cedex, France
Et Bruno Poizat
Affiliation:
Institut Camille Jordan, Université Claude Bernard, 43 Boulevard Du 11 Novembre 1918, 69622 Villeurbanne-Cedex, FranceE-mail:, [email protected] 1.fr

Résumé

We revisit the foundations of positive model theory, introducing h-inductive sentences. These allow a considerably simplified presentation of positive model theory, as well as a characterisation of Hausdorffcats by an amalgamation property of their h-inductive theory.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[2003a] Yaacov, Itaï Ben, Positive model theory and compact abstract theories, Journal of Mathematical Logic, vol. 3 (2003), pp. 85118.CrossRefGoogle Scholar
[2003b] Yaacov, Itaï Ben, Simplicity in compact abstract theories, Journal of Mathematical Logic, vol. 3 (2003), pp. 163191.CrossRefGoogle Scholar
[2003c] Yaacov, Itaï Ben, Thickness, and a categoric point of view of type-space functors, Fundamenta Mathematicae, vol. 179 (2003), pp. 199224.CrossRefGoogle Scholar
[2004] Yaacov, Itaï Ben, Lovely pairs of models: the non first order case, this Journal, vol. 69 (2004), pp. 641662.Google Scholar
[2005] Yaacov, Itaï Ben, Uncountable dense categoricity in cats, this JOurnal, vol. 70 (2005), pp. 829860.Google Scholar
[20??] Yaacov, Itaï Ben and Usvyatsov, Alexander, Continuous first order logic and local stability, 20??Google Scholar
[1973] Chang, Cheng-Chung and Keisler, Jerome H., Model theory, North-Holland, 1973.Google Scholar
[1963] Daigneault, Aubert and Monk, Donald, Representation theory for polyadic algebras, Fundamenta Mathematicae, vol. 52 (1963), pp. 151176.CrossRefGoogle Scholar
[1953] Fraïssé, Roland, Sur certaines relations qui généralisent l'ordre des nombres rationnels, Comptes Rendus de l'Académie des Sciences. Paris, vol. 237 (1953), pp. 540542.Google Scholar
[1993] Hodges, Wilfrid, Model theory, Cambridge University Press, 1993.CrossRefGoogle Scholar
[1997] Hrushovski, Ehud, Simplicity and the Lascar group, prépublication, 1997.Google Scholar
[1956] Jonsson, Bjarni, Universal relational systems, Mathematica Scandinavia, vol. 4 (1956), pp. 193208.CrossRefGoogle Scholar
[1960] Jonsson, Bjarni, Homogeneous universal relational systems, Mathematica Scandinavia, vol. 8 (1960), pp. 137142.CrossRefGoogle Scholar
[1969] Kaiser, Klaus, Über cine Verallgemeinerung der Robinsonschen Modellvervollständigung, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 15 (1969), pp. 3748.CrossRefGoogle Scholar
[1960] Keisler, Jerome H., Theory of models with generalized atomic formulas, this JOurnal, vol. 25 (1960), pp. 126.Google Scholar
[1957] Los, Jerzy and Suszko, R., On the extending of models (IV), Fundamenta Mathematicae, vol. 44 (1957), pp. 343347.CrossRefGoogle Scholar
[1977] Makkai, Michael and Reyes, Gonzalo, First order categorical logic, Lectures Notes in Mathematics, 611, Springer, 1977.CrossRefGoogle Scholar
[1962] Morley, Michael and Vaught, Robert, Homogeneous universal models, Mathematica Scandinavia, vol. 11 (1962), pp. 3757.CrossRefGoogle Scholar
[1998] Mustafin, Tölende, Conditions de Jonsson généralisées et théories de Jonsson généralisées d'algèbres de Boole, Matematicheskie Trudy (Novosibirsk), (1998), pp. 135197, (en russe), traduit en anglais dans Siberian Advances in Mathematics, vol. 10 (2000), pp. 1–58.Google Scholar
[1995] Mustafin, Tölende and Nurkhaidarov, Ermek, Description des théories de Jonsson de polygônes sur un groupe, Sbornik nauchnyh trudov, Qaragandy, 1995, (en russe).Google Scholar
[2002] Mustafin, Yerulan, Quelques propriétés des théories de Jonsson, this JOurnal, vol. 67 (2002), pp. 528536.Google Scholar
[2000] Pillay, Anand, Forking in the category of existentially closed structures, Quaderni di Matematica, vol. 6 (2000).Google Scholar
[2006] Poizat, Bruno, Univers positifs, this JOurnal, vol. 71 (2006), pp. 969976.Google Scholar
[1972] Pouzet, Maurice, Modèle universel d'une théorie n-complète, Comptes Rendus de l'Académie des Sciences. Paris, série A, vol. 274 (1972), pp. 813816.Google Scholar
[1956] Robinson, Abraham, Complete theories, North Holland, 1956.Google Scholar
[1975] Shelah, Saharon, The lazy model-theoretician guide to stability, Logique et Analyse, vol. 71-71 (1975), pp. 241308.Google Scholar
[1949] Tarski, Alfred, Arithmetical classes and types of mathematical systems, Abstracts of papers presented to the American Mathematical Society, vol. 55 (1949), p. 1192.Google Scholar
[1957] Tarski, Alfred and Vaught, Robert, Arithmetical extensions of relational systems, Compositio Mathematica, vol. 13 (1957), pp. 81102.Google Scholar