A note on definability in equational logic
History and Philosophy of Logic 15 (2):189-199 (1994)
| Abstract | After an introduction which demonstrates the failure of the equational analogue of Beth?s definability theorem, the first two sections of this paper are devoted to an elementary exposition of a proof that a functional constant is equationally definable in an equational theory iff every model of the set of those consequences of the theory that do not contain the functional constant is uniquely extendible to a model of the theory itself.Sections three, four and five are devoted to applications and extensions of this result.Topics considered here include equational definability in first order logic, an extended notion of definability in equational logic and the synonymy of equational theories.The final two sections briefly review some of the history of equational logic | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,664 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesWojciech Buszkowski & Ewa Palka (2008). Infinitary Action Logic: Complexity, Models and Grammars. Studia Logica 89 (1):1 - 18.
Stuart M. Shieber, Fernando C. N. Pereira & Mary Dalrymple (1996). Interactions of Scope and Ellipsis. Linguistics and Philosophy 19 (5):527 - 552.
István Németi & Gábor Sági (2000). On the Equational Theory of Representable Polyadic Equality Algebras. Journal of Symbolic Logic 65 (3):1143-1167.
Marius Petria & Răzvan Diaconescu (2006). Abstract Beth Definability in Institutions. Journal of Symbolic Logic 71 (3):1002 - 1028.
B. Courcelle (2012). Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach. Cambridge University Press.
Tomasz Furmanowski (1983). The Logic of Algebraic Rules as a Generalization of Equational Logic. Studia Logica 42 (2-3):251 - 257.
Arnold Beckmann (2002). Proving Consistency of Equational Theories in Bounded Arithmetic. Journal of Symbolic Logic 67 (1):279-296.
William Craig (1989). Near-Equational and Equational Systems of Logic for Partial Functions. II. Journal of Symbolic Logic 54 (4):1181-1215.
William Craig (1989). Near-Equational and Equational Systems of Logic for Partial Functions. I. Journal of Symbolic Logic 54 (3):795-827.
Markus Junker & Ingo Kraus (2002). Theories with Equational Forking. Journal of Symbolic Logic 67 (1):326-340.
Analytics
Monthly downloads
Sorry, there are not enough data points to plot this chart.
|
Added to index2010-08-10Total downloads1 ( #274,602 of 549,013 )Recent downloads (6 months)0How can I increase my downloads? |
My notes
Discussion
