Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/representation-of-mv-algebras-by-regular-ultrapowers-of-0-1-QpC31bVOzI
References (25)
-
D. Mundici (1986)
Interpretation of AF -algebras in ukasiewicz sentential calculusJournal of Functional Analysis
-
(1991)
Representation and reticulation by quotients of MV-algebras -
Marlow Anderson, T. Feil (1988)
Lattice-ordered groups -
(1930)
Comptes Rendus de la Societe de Sciences et des Letters de Varsovie -
V. Weispfenning (1989)
Model Theory of Abelian l -Groups -
B. Gerla (2001)
Many-valued Logics of Continuous t-norms and Their Functional Representation -
L. Belluce, A. Nola, B. Gerla (2007)
Perfect MV-algebras and their LogicApplied Categorical Structures, 15
-
Stephen Jackson (1973)
Model theory of abelian groups -
P. Hájek (1998)
Metamathematics of Fuzzy Logic volume 4 of Trends in Logic, Studia Logica Library -
Chen Chang, H. Keisler (1966)
Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics -
J. Łukasiewicz, A. Tarski (1930)
Untersuchungen über den AussagenkalkülComptes Rendus de la Societe de Sciences Et des Letters de Varsovie, iii
-
R. Cignoli, I. D'Ottaviano, D. Mundici (1999)
Algebraic Foundations of Many-Valued Reasoning -
W. Comfort, S. Negrepontis (1974)
The Theory of Ultrafilters -
C. Chang (1958)
Algebraic analysis of many valued logicsTransactions of the American Mathematical Society, 88
-
P. Hájek (1998)
Metamathematics of Fuzzy Logic, 4
-
(2003)
Tatra Mountains Mathematicals Publications -
L. Belluce, A. Nola, B. Gerla (2008)
Abelian ℓ-Groups with Strong Unit and Perfect MV-AlgebrasOrder, 25
-
(1986)
Interpretation of AF C * algebras in Lukasiewicz sentential calculus -
R. Cignoli, I.M.L. D’Ottaviano, D. Mundici (2000)
Algebraic Foundations of Many-Valued Reasoning, volume 7 of Trends in Logic, Studia Logica Library -
C.C. Chang, J. Keisler (1973)
Model Theory -
(1998)
Metamathematics of Fuzzy Logic, volume 4 of Trends in Logic -
Takuya Kon-no (1998)
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY -
V. Kanovei, S. Shelah (2003)
A definable nonstandard model of the realsJournal of Symbolic Logic, 69
-
A. Nola, P. Belluce (2003)
The MV-algebra of first order Lukasiewicz logic, 27
-
C. Chang (2010)
A NEW PROOF OF THE COMPLETENESS OF THE LUKASIEWICZ AXIOMS^)
- Publisher
- Springer Journals
- Copyright
- Copyright © 2010 by Springer-Verlag
- Subject
- Mathematics; Algebra; Mathematics, general; Mathematical Logic and Foundations
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-010-0182-y
- Publisher site
- See Article on Publisher Site
Abstract
We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0,1]. This result also implies the existence, for any cardinal α, of a single MV-algebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction with iterated ultrapowers, we show how to construct such an algebra of values in a definable way, thus providing a sort of “canonical” set of values for the functional representation.
Journal
Archive for Mathematical Logic – Springer Journals
Published: Mar 16, 2010