Journal of Symbolic Logic 65 (2):857-884 (2000)
|Abstract||Here we investigate the classes RCA $^\uparrow_\alpha$ of representable directed cylindric algebras of dimension α introduced by Nemeti. RCA $^\uparrow_\alpha$ can be seen in two different ways: first, as an algebraic counterpart of higher order logics and second, as a cylindric algebraic analogue of Quasi-Projective Relation Algebras. We will give a new, "purely cylindric algebraic" proof for the following theorems of Nemeti: (i) RCA $^\uparrow_\alpha$ is a finitely axiomatizable variety whenever α ≥ 3 is finite and (ii) one can obtain a strong representation theorem for RCA $^\uparrow_\alpha$ if one chooses an appropriate (non-well-founded) set theory as foundation of mathematics. These results provide a purely cylindric algebraic solution for the Finitization Problem (in the sense of ) in some non-well-founded set theories|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Tarek Sayed Ahmed (2005). Algebraic Logic, Where Does It Stand Today? Bulletin of Symbolic Logic 11 (4):465-516.
István Németi (1991). Algebraization of Quantifier Logics, an Introductory Overview. Studia Logica 50 (3-4):485 - 569.
B. Biró & S. Shelah (1988). Isomorphic but Not Lower Base-Isomorphic Cylindric Set Algebras. Journal of Symbolic Logic 53 (3):846-853.
István Németi & Gábor Sági (2000). On the Equational Theory of Representable Polyadic Equality Algebras. Journal of Symbolic Logic 65 (3):1143-1167.
Yde Venema (1995). Cylindric Modal Logic. Journal of Symbolic Logic 60 (2):591-623.
Roger D. Maddux (1989). Nonfinite Axiomatizability Results for Cylindric and Relation Algebras. Journal of Symbolic Logic 54 (3):951-974.
Jean A. Larson (1985). The Number of One-Generated Cylindric Set Algebras of Dimension Greater Than Two. Journal of Symbolic Logic 50 (1):59-71.
Gábor Sági & Saharon Shelah (2006). On Weak and Strong Interpolation in Algebraic Logics. Journal of Symbolic Logic 71 (1):104 - 118.
I. Németi & A. Simon (2009). Weakly Higher Order Cylindric Algebras and Finite Axiomatization of the Representables. Studia Logica 91 (1):53 - 62.
Gábor Sági (2002). A Note on Algebras of Substitutions. Studia Logica 72 (2):265-284.
Added to index2009-01-28
Total downloads13 ( #87,766 of 548,939 )
Recent downloads (6 months)0
How can I increase my downloads?