Constant Regions in Models of Arithmetic

Notre Dame Journal of Formal Logic 56 (4):603-624 (2015)
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Abstract

This paper introduces a new theory of constant regions, which generalizes that of interstices, in nonstandard models of arithmetic. In particular, we show that two homogeneity notions introduced by Richard Kaye and the author, namely, constantness and pregenericity, are equivalent. This led to some new characterizations of generic cuts in terms of existential closedness.

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10.1215/00294527-3153615

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Moving Intersticial Gaps.James H. Schmerl - 2002 - Mathematical Logic Quarterly 48 (2):283-296.
The Model Theory of Generic Cuts.Richard Kaye & Tin Lok Wong - 2015 - In Åsa Hirvonen, Juha Kontinen, Roman Kossak & Andrés Villaveces (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. Boston: De Gruyter. pp. 281-296.
Generic cuts in models of arithmetic.Richard Kaye - 2008 - Mathematical Logic Quarterly 54 (2):129-144.

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