Generalized functional calculus in lattice-ordered algebras

2014 ◽  
Vol 55 (5) ◽  
pp. 968-976
Author(s):  
B. B. Tasoev
2002 ◽  
Vol 102 (2) ◽  
pp. 215-225
Author(s):  
Teresa Bermύdez ◽  
Manuel González ◽  
Antonio Martinόn

1980 ◽  
Vol 3 (1) ◽  
pp. 105-116
Author(s):  
Bruno Courcelle ◽  
Jean-Claude Raoult

We give a completion theorem for ordered magmas (i.e. ordered algebras with monotone operations) in a general form. Particular instances of this theorem are already known, and new results follow. The semantics of programming languages is the motivation of such investigations.


Author(s):  
Ian Doust ◽  
Qiu Bozhou

AbstractWell-bounded operators are those which possess a bounded functional calculus for the absolutely continuous functions on some compact interval. Depending on the weak compactness of this functional calculus, one obtains one of two types of spectral theorem for these operators. A method is given which enables one to obtain both spectral theorems by simply changing the topology used. Even for the case of well-bounded operators of type (B), the proof given is more elementary than that previously in the literature.


1986 ◽  
Vol 9 (2) ◽  
pp. 218-236 ◽  
Author(s):  
Paul McGuire

2010 ◽  
Vol 362 (1) ◽  
pp. 100-106
Author(s):  
Ian Doust ◽  
Venta Terauds
Keyword(s):  

2001 ◽  
Vol 183 (2) ◽  
pp. 413-450 ◽  
Author(s):  
José Garcı́a-Cuerva ◽  
Giancarlo Mauceri ◽  
Stefano Meda ◽  
Peter Sjögren ◽  
José Luis Torrea
Keyword(s):  

1957 ◽  
Vol 22 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Leon Henkin

The concepts of ω-consistency and ω-completeness are closely related. The former concept has been generalized to notions of Γ-consistency and strong Γ-consistency, which are applicable not only to formal systems of number theory, but to all functional calculi containing individual constants; and in this general setting the semantical significance of these concepts has been studied. In the present work we carry out an analogous generalization for the concept of ω-completeness.Suppose, then, that F is an applied functional calculus, and that Γ is a non-empty set of individual constants of F. We say that F is Γ-complete if, whenever B(x) is a formula (containing the single free individual variable x) such that ⊦ B(α) for every α in Γ, then also ⊦ (x)B(x). In the paper “Γ-con” a sequence of increasingly strong concepts, Γ-consistency, n = 1,2, 3,…, was introduced; and it is possible in a formal way to define corresponding concepts of Γn-completeness, as follows. We say that F is Γn-complete if, whenever B(x1,…, xn) is a formula (containing exactly n distinct free variables, namely x1…, xn) such that ⊦ B(α1,…,αn) for all α1,…,αn in Γ, then also ⊦ (X1)…(xn)B(x1,…,xn). However, unlike the situation encountered in the paper “Γ-con”, these definitions are not of interest – for the simple reason that F is Γn-complete if and only if it is Γ-complete, as one easily sees.


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