Mathematical Logic Quarterly 46 (4):505-516 (2000)

In this paper we study the model theory of extensions of models of first-order Peano Arithmetic by means of the arithmetized completeness theorem applied to a definable complete extension of PA in the original model. This leads us to many interesting model theoretic properties equivalent to reflection principles and ω-consistency, and these properties together with the associated first-order schemes extending PA are studied
Keywords ω‐consistency  Reflection principles  Arithmetized completeness theorem  End‐extensions  Models of arithmetic
Categories (categorize this paper)
DOI 10.1002/1521-3870(200010)46:4
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 63,323
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Local Reflection, Definable Elements and 1-Provability.Evgeny Kolmakov - 2020 - Archive for Mathematical Logic 59 (7-8):979-996.

Add more citations

Similar books and articles

Nonstandard Models and Kripke's Proof of the Gödel Theorem.Hilary Putnam - 2000 - Notre Dame Journal of Formal Logic 41 (1):53-58.
Two Applications of Boolean Models.Thierry Coquand - 1998 - Archive for Mathematical Logic 37 (3):143-147.
A Topological Completeness Theorem.Carsten Butz - 1999 - Archive for Mathematical Logic 38 (2):79-101.
Blunt and Topless End Extensions of Models of Set Theory.Matt Kaufmann - 1983 - Journal of Symbolic Logic 48 (4):1053-1073.
Undecidability and Intuitionistic Incompleteness.D. C. McCarty - 1996 - Journal of Philosophical Logic 25 (5):559 - 565.
Interpretability Over Peano Arithmetic.Claes Strannegård - 1999 - Journal of Symbolic Logic 64 (4):1407-1425.
Resplendent Models and $${\sigma_1^1}$$ -Definability with an Oracle.Andrey Bovykin - 2008 - Archive for Mathematical Logic 47 (6):607-623.
Basic Predicate Calculus.Wim Ruitenburg - 1998 - Notre Dame Journal of Formal Logic 39 (1):18-46.
Completeness and Incompleteness for Intuitionistic Logic.Charles McCarty - 2008 - Journal of Symbolic Logic 73 (4):1315-1327.


Added to PP index

Total views
29 ( #376,569 of 2,448,712 )

Recent downloads (6 months)
1 ( #445,641 of 2,448,712 )

How can I increase my downloads?


My notes