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Brown, C. and D. Gurr. Relations and noncommutative linear logic. J. of Pure and Applied Algebra, 105, 2, pp.: 117-136, 1995.

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Explicit Substitution into Action - Non-Monotone Logic For   (Correct)

....(L L) L R) #,# # # #, #, # (R# L) R# R) Table 1. A sequent system for LP # . are the natural generalizations of the rules given by Girard for the commutative intuitionistic linear logic, cf. 14, 15] to the non commutative case, cf [6]. The exceptional axiom is (#) Its expected generalization is #, A, as in [6] However, the stronger axiom is not consistent with our earlier discussion, and axiom (16) in particular. For instance ldd = yes would then be equivalent to rather than ldd = yes. Consequently, it will not be ....

....(R# R) Table 1. A sequent system for LP # . are the natural generalizations of the rules given by Girard for the commutative intuitionistic linear logic, cf. 14, 15] to the non commutative case, cf [6] The exceptional axiom is (#) Its expected generalization is #, A, as in [6]. However, the stronger axiom is not consistent with our earlier discussion, and axiom (16) in particular. For instance ldd = yes would then be equivalent to rather than ldd = yes. Consequently, it will not be valid in our intended interpretation. Embedding the usual logic of predicates into ....

Brown, C. and D. Gurr. Relations and noncommutative linear logic. J. of Pure and Applied Algebra, 105, 2, pp.: 117-136, 1995.


Profinite Methods in Semigroup Theory - Weil (2000)   (4 citations)  (Correct)

....fact that this property of groups can be seen as a strengthening of the LERF property. The geometric ideas mentioned above gave rise to a number of developments, notably concerning the relativization of Rhodes conjecture to other pseudovarieties of groups. Following work by Gildenhuys and Ribes [42], Almeida and Weil characterized the pseudovarieties of groups H such that the profinite Cayley graph of FA (H) is a profinite tree, which they termed arborescent pseudovarieties: they are exactly the pseudovarieties H such that if G=N 2 H and N 2 H Ab, then G 2 H [20, 21] In particular, every ....

D. Gildenhuys and L. Ribes. Profinite groups and Boolean graphs, J. Pure and Applied Algebra 12 (1978) 21--47.


Primer on CPP Geometry - Greenberg   (Correct)

....Greenberg Institut Fourier, Grenoble Our purpose is to describe some basic ideas and constructions in C 1 , piecewise projective (CPP for short) geometry on the circle. This geometry seems to provide a good context in which to discuss (see definition 1. 1) the Higman Thompson group G (see [Br], GhS] and certain of its subgroups (see [G2] This report was written during a visit to the SFB at the University of Bielefeld, to which I am very grateful. Conversations with Ross Geoghegan and Vlad Sergiescu were both encouraging and helpful. 0.1 Introduction We require some notation. ....

....2 R) K 2 R=f Gamma1; Gamma1g. Thus we can give (2.11) a direct geometric proof that K 2 R=f Gamma1; Gamma1g is divisible. Let G = fg 2 CPP (S 1 ) g l x ; g r x 2 PSL 2 Z; x 2 S 1 ; and k(g) Q [ f1gg: It was pointed out by Thurston that G is the Higman Thompson group ([Br], GhS] studied in different guises in group theory, logic and dynamical systems. Part 3 of this report describes a space T g on which G acts, with discrete orbits and finitely generated stabilizers. As an application, we obtain an explicit K(F 0 ; 1) where F 0 = fg 2 G; g l 1 = g r 1 = ....

K.Brown: Finiteness Properties of Groups, J. Pure and Applied Algebra 44(1987), 45--75.

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