David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 73 (3):337 - 365 (2003)
A Dedekind Algebra is an ordered pair (B,h) where B is a non-empty set and h is an injective unary function on B. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called configurations of the Dedekind algebra. There are N0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on omega called its configuration signature. The configuration signature of a Dedekind algebra counts the number of configurations in the decomposition of the algebra in each isomorphism type.The configuration signature of a Dedekind algebra encodes the structure of that algebra in the sense that two Dedekind algebras are isomorphic iff their configuration signatures are identical. Configuration signatures are used to establish various results in the first-order model theory of Dedekind algebras. These include categoricity results for the first-order theories of Dedekind algebras and existence and uniqueness results for homogeneous, universal and saturated Dedekind algebras. Fundamental to these results is a condition on configuration signatures that is necessary and sufficient for elementary equivalence.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Robert S. Lubarsky & Michael Rathjen (2008). On the Constructive Dedekind Reals. Logic and Analysis 1 (2):131-152.
George Weaver (2011). A General Setting for Dedekind's Axiomatization of the Positive Integers. History and Philosophy of Logic 32 (4):375-398.
A. C. Walczak-Typke (2005). The First-Order Structure of Weakly Dedekind-Finite Sets. Journal of Symbolic Logic 70 (4):1161 - 1170.
Anand Pillay & Charles Steinhorn (1987). On Dedekind Complete o-Minimal Structures. Journal of Symbolic Logic 52 (1):156-164.
Sergiu Rudeanu (1993). On Łukasiewicz-Moisil Algebras of Fuzzy Sets. Studia Logica 52 (1):95 - 111.
Ansten Klev (2011). Dedekind and Hilbert on the Foundations of the Deductive Sciences. Review of Symbolic Logic 4 (4):645-681.
V. Yu Shavrukov (1997). Undecidability in Diagonalizable Algebras. Journal of Symbolic Logic 62 (1):79-116.
Erich H. Reck (2003). Dedekind's Structuralism: An Interpretation and Partial Defense. Synthese 137 (3):369 - 419.
George Weaver (2000). Homogeneous and Universal Dedekind Algebras. Studia Logica 64 (2):173-192.
Added to index2009-01-28
Total downloads14 ( #130,846 of 1,679,387 )
Recent downloads (6 months)1 ( #183,003 of 1,679,387 )
How can I increase my downloads?