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AN EXPOSITION OF THE COMPACTNESS OF $L({Q^{\mathrm{cf}}})$

Published online by Cambridge University Press:  11 June 2020

ENRIQUE CASANOVAS
Affiliation:
DEPARTAMENT DE MATEMÀTIQUES I INFORMÀTICA UNIVERSITAT DE BARCELONA GRAN VIA 585, E-08007BARCELONA, SPAIN E-mail: e.casanovas@ub.edu
MARTIN ZIEGLER
Affiliation:
ALBERT-LUDWIGS-UNIVERSITÄT FREIBURG MATHEMATISCHES INSTITUT ABTEILUNG FÜR MATHEMATISCHE LOGIK ECKERSTR. 1, 79104FREIBURG, GERMANY E-mail: ziegler@uni-freiburg.de

Abstract

We give an exposition of the compactness of $L({Q^{\mathrm{\,cf}}\!\!\!\!\!\!}_{C})$ , for any set C of regular cardinals.

Type
Articles
Copyright
© The Association for Symbolic Logic 2020

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References

REFERENCES

Casanovas, E. and Shelah, S., Universal theories and compactly expandable models . The Journal of Symbolic Logic , vol. 84 (2019) pp. 12151223.CrossRefGoogle Scholar
Chang, C. C. and Keisler, H. J., Model Theory , third ed., North Holland, Amsterdam, 1990.Google Scholar
Ebbinghaus, H.-D., Extended logics: The general framework , Model–Theoretic Logics (Barwise, J. and Feferman, S., editors), Springer Verlag, New York, 1985, pp. 2576.Google Scholar
Hodkinson, I., Book review—Models and games by J. Väänänen , this Journal , vol. 18 (2012), pp. 406408.Google Scholar
Keisler, H. J., Logic with the quantifier “there exist uncountably many” . Annals of Mathematical Logic , vol. 1 (1970), pp. 193.CrossRefGoogle Scholar
Makowsky, J. A. and Shelah, S., The theorems of Beth and Craig in abstract model theory. II . Archiv für Mathematische Logik und Grundlagenforschung , vol. 21 (1981), pp. 1335.CrossRefGoogle Scholar
Shelah, S., On models with power like orderings . The Journal of Symbolic Logic , vol. 37 (1972), pp. 247267.CrossRefGoogle Scholar
Shelah, S., Generalized quantifiers and compact logic . Transactions of the American Mathematical Society , vol. 204 (1975), pp. 342364.CrossRefGoogle Scholar
Tent, K. and Ziegler, M., A Course in Model Theory , Lecture Notes in Logic, vol. 40, Cambridge University Press, Cambridge, 2012.CrossRefGoogle Scholar
Väänänen, J., Models and games , Cambridge Studies in Advanced Mathematics, vol. 132, Cambridge University Press, Cambridge, 2011.CrossRefGoogle Scholar