caa a22 4500 388039558 CHVBK 20180307125017.0 cr unu---uuuuu 161130e199803 xx s 000 0 eng 10.2307/2586595 doi S0022481200015401 pii (NATIONALLICENCE)cambridge-10.2307/2586595 Relativised quantification: Some canonical varieties of sequence-set algebras [Elektronische Daten] This paper explores algebraic aspects of two modifications of the usual account of first-order quantifiers. Standard first-order quantificational logic is modelled algebraically by cylindric algebras. Prime examples of these are algebras whose members are sets of sequences: given a first-order model U for a language that is based on the set {υκ: κ < α} of variables, each formula φ is represented by the set of all those α-length sequences x = 〈x κ: κ < α〉 that satisfy φ in U. Such a sequence provides a value-assignment to the variables (υκ is assigned value x κ), but it may also be viewed geometrically as a point in the α-dimensional Cartesian space α U of all α-length sequences whose terms come from the underlying set U of U. Then existential quantification is represented by the operation of cylindrification. To explain this, define a binary relation T κ on sequences by putting x T κ y if and only if x and y differ at most at their κth coordinate, i.e., Then for any set X ⊆ α U, the set is the "cylinder” generated by translation of X parallel to the κth coordinate axis in α U. Given the standard semantics for the existential quantifier ∃υκ as it is evident that Copyright © Association for Symbolic Logic 1998 Andréka Hajnal Mathematical Institute of The Hungarian Academy of Sciences, P. O. Box 127, H-1364 Budapest, Hungary, E-mail: andreka@math-inst.hu Goldblatt Robert School of Mathematical and Computing Sciences, Victoria University, P. O. Box 600, Wellington, New Zealand, E-mail: Rob.Goldblatt@vuw.ac.nz Németi István Mathematical Institute of the Hungarian Academy of Sciences, P. O. Box 127, H-1364 Budapest, Hungary, E-mail: nemeti@math-inst.hu The Journal of Symbolic Logic Cambridge University Press 63/1(1998-03), 163-184 0022-4812 63:1<163 1998 63 JSL https://doi.org/10.2307/2586595 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586595 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Andréka Hajnal Mathematical Institute of The Hungarian Academy of Sciences, P. O. Box 127, H-1364 Budapest, Hungary, E-mail: andreka@math-inst.hu NATIONALLICENCE 700 1- Goldblatt Robert School of Mathematical and Computing Sciences, Victoria University, P. O. Box 600, Wellington, New Zealand, E-mail: Rob.Goldblatt@vuw.ac.nz NATIONALLICENCE 700 1- Németi István Mathematical Institute of the Hungarian Academy of Sciences, P. O. Box 127, H-1364 Budapest, Hungary, E-mail: nemeti@math-inst.hu NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/1(1998-03), 163-184 0022-4812 63:1<163 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge