Tolerant sequence

Tolerant sequence

In mathematical logic, a tolerant sequence is a sequence

:T_1,...,T_n

of formal theories such that there are consistent extensions

:S_1,...,S_n

of these theories with each S_{i+1} interpretable in S_i. Tolerance naturally generalizes from sequences of theories to trees of theories. Weak interpretability can be shown to be a special, binary case of tolerance.

This concept, together with its dual concept of cotolerance, was introduced by [http://www.csc.villanova.edu/~japaridz/ Japaridze] in 1992, who also proved that, for Peano arithmetic and any stronger theories with effective axiomatizations, tolerance is equivalent to Pi_1-consistency.

See also

*Interpretability
*Cointerpretability
*Interpretability logic

References

* [http://www.csc.villanova.edu/~japaridz/ G.Japaridze] , "The logic of linear tolerance". Studia Logica 51 (1992), pp. 249-277.
* [http://www.csc.villanova.edu/~japaridz/ G.Japaridze] , "A generalized notion of weak interpretability and the corresponding logic". Annals of Pure and Applied Logic 61 (1993), pp. 113-160.
* [http://www.csc.villanova.edu/~japaridz/study.html G.Japaridze] and D. de Jongh, "The logic of provability". Handbook of Proof Theory. S.Buss, ed. Elsevier, 1998, pp. 476-546.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • Peptide sequence tag — A peptide sequence tag is a piece of information about a peptide obtained by tandem mass spectrometry that can be used to identify this peptide in a protein database.cite journal |author=Hardouin J |title=Protein sequence information by matrix… …   Wikipedia

  • Lollipop sequence numbering — is a numbering scheme used in routing protocols. In this numbering scheme, sequence numbers start at a negative value, increase until they reach zero, then cycles through a finite set of positive numbers indefinitely. When a system is rebooted,… …   Wikipedia

  • List of mathematics articles (T) — NOTOC T T duality T group T group (mathematics) T integration T norm T norm fuzzy logics T schema T square (fractal) T symmetry T table T theory T.C. Mits T1 space Table of bases Table of Clebsch Gordan coefficients Table of divisors Table of Lie …   Wikipedia

  • List of mathematical logic topics — Clicking on related changes shows a list of most recent edits of articles to which this page links. This page links to itself in order that recent changes to this page will also be included in related changes. This is a list of mathematical logic …   Wikipedia

  • BIBLE — THE CANON, TEXT, AND EDITIONS canon general titles the canon the significance of the canon the process of canonization contents and titles of the books the tripartite canon …   Encyclopedia of Judaism

  • Ralstonia eutropha — Scientific classification Kingdom: Bacteria Phylum: Proteobacteria Class: Beta Proteobacteria …   Wikipedia

  • literature — /lit euhr euh cheuhr, choor , li treuh /, n. 1. writings in which expression and form, in connection with ideas of permanent and universal interest, are characteristic or essential features, as poetry, novels, history, biography, and essays. 2.… …   Universalium

  • Life Sciences — ▪ 2009 Introduction Zoology       In 2008 several zoological studies provided new insights into how species life history traits (such as the timing of reproduction or the length of life of adult individuals) are derived in part as responses to… …   Universalium

  • India — /in dee euh/, n. 1. Hindi, Bharat. a republic in S Asia: a union comprising 25 states and 7 union territories; formerly a British colony; gained independence Aug. 15, 1947; became a republic within the Commonwealth of Nations Jan. 26, 1950.… …   Universalium

  • IMMUNITÉ ET SYSTÈME IMMUNITAIRE — Le système immunitaire assume l’une des grandes fonctions physiologiques des Vertébrés: l’aptitude à la reconnaissance d’un nombre prodigieux de structures moléculaires distinctes, les antigènes. Un antigène est classiquement réputé « étranger »… …   Encyclopédie Universelle

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”