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On compactness of logics that can express properties of symmetry or connectivity
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Helsingfors Universitet.
2015 (English)In: Studia Logica: An International Journal for Symbolic Logic, ISSN 0039-3215, E-ISSN 1572-8730, Vol. 103, no 1, 1-20 p.Article in journal (Refereed) Published
Abstract [en]

A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to prove that for a number of natural properties P speaking about automorphism groups or connectivity, every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The basic idea underlying the results and examples presented here is that it is possible to construct a countable first-order theory T such that every model of T has a very rich automorphism group, but every finite subset T' of T has a model which is rigid.

Place, publisher, year, edition, pages
Springer, 2015. Vol. 103, no 1, 1-20 p.
Keyword [en]
Abstract logic, Model theoretic logic, Compactness, Completeness, Automorphism, Connectivity, Random graph theory
National Category
Algebra and Logic
Research subject
Mathematical Logic
Identifiers
URN: urn:nbn:se:uu:diva-244545DOI: 10.1007/s11225-013-9522-3ISI: 000349360100001OAI: oai:DiVA.org:uu-244545DiVA: diva2:789135
Available from: 2015-02-17 Created: 2015-02-17 Last updated: 2017-12-04Bibliographically approved

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Koponen, Vera

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