Abstract
We show that any model \(\mathfrak{A}\) can be extended, in a canonical way, to a model \(\beta\mathfrak{A}\) consisting of ultrafilters over it. The extension procedure preserves homomorphisms: any homomorphism of \(\mathfrak{A}\) into \(\mathfrak{B}\) extends to a continuous homomorphism of \(\beta\mathfrak{A}\) into \(\beta\mathfrak{B}\). Moreover, if a model \(\mathfrak{B}\) carries a compact Hausdorff topology which is (in a certain sense) compatible, then any homomorphism of \(\mathfrak{A}\) into \(\mathfrak{B}\) extends to a continuous homomorphism of \(\beta\mathfrak{A}\) into \(\mathfrak{B}\). This is also true for embeddings instead of homomorphisms.
Partially supported by an INFTY grant of ESF.
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© 2011 Springer-Verlag Berlin Heidelberg
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Saveliev, D.I. (2011). Ultrafilter Extensions of Models. In: Banerjee, M., Seth, A. (eds) Logic and Its Applications. ICLA 2011. Lecture Notes in Computer Science(), vol 6521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18026-2_14
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DOI: https://doi.org/10.1007/978-3-642-18026-2_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18025-5
Online ISBN: 978-3-642-18026-2
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