Truth in generic cuts

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Truth in generic cuts. / Kaye, Richard; Wong, TL.

In: Annals of Pure and Applied Logic, Vol. 161, No. 8, 01.05.2010, p. 987-1005.

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Kaye, Richard ; Wong, TL. / Truth in generic cuts. In: Annals of Pure and Applied Logic. 2010 ; Vol. 161, No. 8. pp. 987-1005.

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@article{8f65f04204614db7bab5267b41cd256e,
title = "Truth in generic cuts",
abstract = "In an earlier paper (MLQ 54,129-144) the first author initiated the study of generic cuts of a model of Peano arithmetic relative to a notion of an indicator in the model. This paper extends that work. We generalise the idea of an indicator to a related neighbourhood system; this allows the theory to be extended to one that includes the case of elementary cuts. Most results transfer to this more general context, and in particular we obtain the idea of a generic cut relative to a neighbourhood system, which is studied in more detail. The main new result on generic cuts presented here is a description of truth in the structure (M. I), where 1 is a generic cut of a model M of Peano arithmetic. The special case of elementary generic cuts provides a partial answer to a question of Kossak [R. Kossak, Four problems concerning recursively saturated models of arithmetic, Notre Dame Journal of Formal Logic 36(4) (1995) 519-530]. (C) 2010 Published by Elsevier B.V.",
keywords = "Peano arithmetic, Generic cuts",
author = "Richard Kaye and TL Wong",
year = "2010",
month = may,
day = "1",
doi = "10.1016/j.apal.2009.11.001",
language = "English",
volume = "161",
pages = "987--1005",
journal = "Annals of Pure and Applied Logic",
issn = "0168-0072",
publisher = "Elsevier",
number = "8",

}

RIS

TY - JOUR

T1 - Truth in generic cuts

AU - Kaye, Richard

AU - Wong, TL

PY - 2010/5/1

Y1 - 2010/5/1

N2 - In an earlier paper (MLQ 54,129-144) the first author initiated the study of generic cuts of a model of Peano arithmetic relative to a notion of an indicator in the model. This paper extends that work. We generalise the idea of an indicator to a related neighbourhood system; this allows the theory to be extended to one that includes the case of elementary cuts. Most results transfer to this more general context, and in particular we obtain the idea of a generic cut relative to a neighbourhood system, which is studied in more detail. The main new result on generic cuts presented here is a description of truth in the structure (M. I), where 1 is a generic cut of a model M of Peano arithmetic. The special case of elementary generic cuts provides a partial answer to a question of Kossak [R. Kossak, Four problems concerning recursively saturated models of arithmetic, Notre Dame Journal of Formal Logic 36(4) (1995) 519-530]. (C) 2010 Published by Elsevier B.V.

AB - In an earlier paper (MLQ 54,129-144) the first author initiated the study of generic cuts of a model of Peano arithmetic relative to a notion of an indicator in the model. This paper extends that work. We generalise the idea of an indicator to a related neighbourhood system; this allows the theory to be extended to one that includes the case of elementary cuts. Most results transfer to this more general context, and in particular we obtain the idea of a generic cut relative to a neighbourhood system, which is studied in more detail. The main new result on generic cuts presented here is a description of truth in the structure (M. I), where 1 is a generic cut of a model M of Peano arithmetic. The special case of elementary generic cuts provides a partial answer to a question of Kossak [R. Kossak, Four problems concerning recursively saturated models of arithmetic, Notre Dame Journal of Formal Logic 36(4) (1995) 519-530]. (C) 2010 Published by Elsevier B.V.

KW - Peano arithmetic

KW - Generic cuts

U2 - 10.1016/j.apal.2009.11.001

DO - 10.1016/j.apal.2009.11.001

M3 - Article

VL - 161

SP - 987

EP - 1005

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

SN - 0168-0072

IS - 8

ER -