Abstract
1.1 Provability in Logic Stig Kanger’s small book from 1957, Provability in Logic, contains eight chapters. The last two chapters are concerned with modal logic. This part has received considerable attention and recognition. Chapters 2–6 treat elementary extensional logic. This part has drawn scantier attention. The present essay contains an exposition and comments on chapters 2–5, with an emphasis on the contributions to set theory and model theory. I take for granted that the reader has access to Provability in Logic, either the original edition from 1957 or the reprint in Collected Papers of Stig Kanger, Vol. I.
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References
Aczel, P. (1988), Non-Well-Founded Sets. Center for the Study of Language and Information, Stanford.
Barwise, J., and J. Etchemendy (1987), The Liar: An Essay on Truth and Circular Propositions. Oxford UP, Oxford.
Drake, F. R. (1974), Set Theory: An Introduction to Large Cardinals. North-Holland Publishing Company, Amsterdam.
Fischer, F. H. (1958), “Review of Provability in Logic”. Journal of Symbolic Logic, 23, 37–38.
Fitting, M. (1996), First-Order Logic and Automated Theorem Proving. Second edition. Springer-Verlag, Berlin.
Kanger, S. (1957), Provability in Logic. Acta Universitatis Stockholmiensis. Almqvist & Wiksell, Stockholm.
Lindström, Ingrid (1986), “A Construction of Non-Well-Founded Sets Within Martin-Lüf s Type Theory.” Department of Mathematics, Uppsala University.
Mirimanoff, D. (1917a), “Les antinomies de Russell et de Burali-Forti et le problème fundamental de la theorie des ensembles.” L’enseignement mathematique, 19, 37–52.
Mirimanoff, D. (1917b), “Remarques sur la theorie des ensembles.” L’enseignement mathématique, 19, 209–217.
Nerode, A., and R. A. Shore (1997), Logic for Applications. Second edition. Springer-Verlag, Berlin.
Zermelo, E. (1908), “Untersuchungen über die Grundlagen der Mengenlehre, I.” Mathematische Annalen, 65, 261–281.
Zermelo, E. (1930), “Über Grenzzahlen und Mengenbereiche.” Fundamenta mathematical 16, 29–47.
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Hansen, K.B. (2001). Kanger’s Ideas on Non-Well-Founded Sets: Some Remarks. In: Holmström-Hintikka, G., Lindström, S., Sliwinski, R. (eds) Collected Papers of Stig Kanger with Essays on His Life and Work. Synthese Library, vol 304. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0630-9_5
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DOI: https://doi.org/10.1007/978-94-010-0630-9_5
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