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Pure-injectivity and model theory for G-sets

Published online by Cambridge University Press:  12 March 2014

Ravi Rajani  and
Mike Prest
Ravi Rajani
Affiliation:
School of Mathematics, Alan Turing Building, University of Manchester, Manchester, M13 9Pl, UK, E-mail: ravi.inajar@googlemail.com, E-mail: mprest@manchester.ac.uk
Mike Prest
Affiliation:
School of Mathematics, Alan Turing Building, University of Manchester, Manchester, M13 9Pl, UK, E-mail: ravi.inajar@googlemail.com, E-mail: mprest@manchester.ac.uk
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Abstract

In the model theory of modules the Ziegler spectrum, the space of indecomposable pure-injective modules, has played a key role. We investigate the possibility of defining a similar space in the context of G-sets where G is a group.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 2 , June 2009 , pp. 474 - 488
Copyright
Copyright © Association for Symbolic Logic 2009

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References

REFERENCES

[1]Adámek, J. and Rosický, J., Locally presentable and accessible categories, London Mathematical Society Lecture Notes Series, vol. 189, Cambridge University Press, 1994.CrossRefGoogle Scholar
[2]Banaschewski, B., Equational compactness of G-sets, Canadian Mathematical Bulletin, vol. 17 (1974), no. 1, pp. 11–18.CrossRefGoogle Scholar
[3]Hodges, W., Model theory, Encyclopedia of Mathematics and Applications, vol. 42, Cambridge University Press, 1993.CrossRefGoogle Scholar
[4]Jensen, C. U. and Lenzing, H., Model theoretic algebra; with particular emphasis on fields, rings and modules, Gordon and Breach, 1989.Google Scholar
[5]Keisler, H. J. and Chang, C. C., Model theory, third ed., Studies in Logic and Foundations of Mathematics, vol. 73, Elsevier Science Publishers B.V., 1990.CrossRefGoogle Scholar
[6]Lane, S. Mac and Moerdijk, I., Sheaves in geometry and logic, Springer-Verlag, 1992.Google Scholar
[7]Mycielski, J. and Ryll-Nardzewski, C., Equationally compact algebras II, Fundamenta Mathematicae, vol. 61 (1968), pp. 271–281.CrossRefGoogle Scholar
[8]Prest, M., Model theory and modules, London Mathematical Society Lecture Notes Series, vol. 130, Cambridge University Press, 1988.CrossRefGoogle Scholar
[9]Prest, M., Purity, spectra and localisation, in press.Google Scholar
[10]Rajani, R. and Prest, M., Model-theoretic imaginaries and coherent sheaves, submitted.Google Scholar
[11]Taylor, W., Review of [2], Mathematical Reviews, MR0351954 (50 no. 4442).Google Scholar
[12]Wenzel, G. H., Equational compactness, Universal algebra (Grätzer, G., editor), Springer-Verlag, second ed., 1979, pp. 417–447.Google Scholar
[13]Ziegler, M., Model theory and modules, Annals of Pure and Applied Logic, vol. 26 (1984), pp. 149–213.CrossRefGoogle Scholar