On compactness of logics that can express properties of symmetry or connectivity
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
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.
Abstract logic, Model theoretic logic, Compactness, Completeness, Automorphism, Connectivity, Random graph theory
Algebra and Logic
Research subject Mathematical Logic
IdentifiersURN: urn:nbn:se:uu:diva-244545DOI: 10.1007/s11225-013-9522-3ISI: 000349360100001OAI: oai:DiVA.org:uu-244545DiVA: diva2:789135