Truth in generic cuts

Annals of Pure and Applied Logic 161 (8):987-1005 (2010)
  Copy   BIBTEX


In an earlier paper 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 , where I 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 36 519–530]



    Upload a copy of this work     Papers currently archived: 92,227

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Type two cuts, bad cuts and very bad cuts.Renling Jin - 1997 - Journal of Symbolic Logic 62 (4):1241-1252.
Generic cuts in models of arithmetic.Richard Kaye - 2008 - Mathematical Logic Quarterly 54 (2):129-144.
Generic terms and generic sentences.Greg N. Carlson - 1982 - Journal of Philosophical Logic 11 (2):145 - 181.
The distribution of the generic recursively enumerable degrees.Ding Decheng - 1992 - Archive for Mathematical Logic 32 (2):113-135.
Alethic pluralism, generic truth, and mixed conjunctions.Roy T. Cook - 2011 - Philosophical Quarterly 61 (244):624-629.
Normal derivations and sequent derivations.Mirjana Borisavljevi - 2008 - Journal of Philosophical Logic 37 (6):521 - 548.
Complexity of the -query Tautologies in the Presence of a Generic Oracle.Toshio Suzuki - 2000 - Notre Dame Journal of Formal Logic 41 (2):142-151.
Subclasses of the Weakly Random Reals.Johanna N. Y. Franklin - 2010 - Notre Dame Journal of Formal Logic 51 (4):417-426.
The degrees below a 1-generic degree $.Christine Ann Haught - 1986 - Journal of Symbolic Logic 51 (3):770 - 777.
Cuts in hyperfinite time lines.Renling Jin - 1992 - Journal of Symbolic Logic 57 (2):522-527.
Almost weakly 2-generic sets.Stephen A. Fenner - 1994 - Journal of Symbolic Logic 59 (3):868-887.


Added to PP

104 (#169,303)

6 months
9 (#317,143)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

On Cofinal Submodels and Elementary Interstices.Roman Kossak & James H. Schmerl - 2012 - Notre Dame Journal of Formal Logic 53 (3):267-287.
Constant Regions in Models of Arithmetic.Tin Lok Wong - 2015 - Notre Dame Journal of Formal Logic 56 (4):603-624.

Add more citations