Model theory of the inaccessibility scheme

Archive for Mathematical Logic 50 (7-8):697-706 (2011)
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Abstract

Suppose L = { <,...} is any countable first order language in which < is interpreted as a linear order. Let T be any complete first order theory in the language L such that T has a κ-like model where κ is an inaccessible cardinal. Such T proves the Inaccessibility Scheme. In this paper we study elementary end extensions of models of the inaccessibility scheme.

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10.1007/s00153-011-0242-y

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End extensions and numbers of countable models.Saharon Shelah - 1978 - Journal of Symbolic Logic 43 (3):550-562.
Models with Orderings.H. J. Keisler, B. van Rootselaar & J. F. Staal - 1974 - Journal of Symbolic Logic 39 (2):334-335.
Model theory of the regularity and reflection schemes.Ali Enayat & Shahram Mohsenipour - 2008 - Archive for Mathematical Logic 47 (5):447-464.
On Keisler singular‐like models.Shahram Mohsenipour - 2008 - Mathematical Logic Quarterly 54 (3):330-336.

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