CUBO A Mathematical Journal Vol.13, Nº02, (59-72). June 2011

On λ strong homogeneity existence for cofinality logic

Saharon Shelah ¹
Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel. email: shelah@math.huji.ac.il
url: http://shelah.logic.at

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ABSTRACT
Let C Reg be a non-empty class (of regular cardinals). Then the logic has additional nice properties: it has the homogeneous model existence property.

Keywords and phrases: Model theory, soft model theory, cofinality quantifier.

Mathematics Subject Classification: 03C95, 03C80.

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RESUMEN
Sea C Reg una clase no vacía (de cardinales regulares). Entonces la lógica tiene propiedades adicionales: Esta tiene la propiedad de modelo existencia homogénea.

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¹The author thanks Alice Leonhardt for the beautiful typing. The author would like to thank the Israel Science
Foundation for partial support of this research (Grants No. 451/99 and 710/07). Publication 750.

Referencias
[Mak85] Johann A. Makowsky, Compactnes, embeddings and definability, Model-Theoretic Logics (J. Barwise and S. Feferman, eds.), Springer-Verlag, 1985, pp. 645-716.

[Sh:h] Saharon Shelah, Classification Theory for Abstract Elementary Classes, Studies in Logic: Mathematical logic and foundations, vol. 18, College Publications, 2009.

[Sh:3] Finite diagrams stable in power, Annals of Mathematical Logic 2 (1970), 69-118.

[Sh:43] Generalized quantifiers and compact logic, Transactions of the American Mathematical Society 204 (1975), 342-364.

[Sh:54] The lazy model-theoretician's guide to stability, Logique et Analyse 18 (1975), 241-308.

[Sh:88r] Abstract elementary classes near , Chapter I Studies in Logic, College Publ. 18 (2009). 0705.4137. 0705.4137.

[MkSh:166] Alan H. Mekler and Saharon Shelah, Stationary logic and its friends. I, Notre Dame Journal of Formal Logic 26 (1985), 129-138, Proceedings of the 1980/1 Jerusalem Model Theory year.

[Sh:199] Saharon Shelah, Remarks in abstract model theory, Annals of Pure and Applied Logic 29 (1985), 255-288.

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Received: April 2009. Revised: December 2009.