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In this paper we investigate the dependence of recursively enumerable structures on the equality relation which is fixed to a specific r.e. equivalence relation. We compare r.e. equivalence relations on the natural numbers with respect to the amount of structures they permit to represent from a given class of structures such as algebras, permutations and linear orders. In particular, we show th...

We study fragments of Allen’s algebra that contain a basic relation distinct from the equality relation. We prove that such a fragment is either NPcomplete or else contained in some already known tractable subalgebra. We obtain this result by giving a new uniform description of known maximal tractable subalgebras and then systematically using an algebraic technique for description of maximal su...

Energy dissipation in a nonequilibrium steady state is studied in driven quantum Langevin systems. We analyze a characteristic function that generates energy dissipation flow to thermal environment. This function gives a general formula for the average rate of energy dissipation using an autocorrelation function for the system variable. This leads to a general expression of the equality that co...

We investigate the expressive power of sentences of the family of independence-friendly (IF) logics in the equality-free setting. Various natural equality-free fragments of logics in this family translate into the version of existential second-order logic with prenex quantification of function symbols only and with the first-order parts of formulae equality-free. We study this version of existe...

Let R be a convergent term rewriting system, and let CR-equality on (simply typed) combinatory logic terms be the equality induced by βηRequality on terms of the (simply typed) lambda calculus under any of the standard translations between these two frameworks for higher-order reasoning. We generalize the classical notion of strong reduction to a reduction relation which generates CR-equality a...

..................................................................................................... 3 Sammanfattning på svenska ....................................................................... 5 Original papers ........................................................................................... 7 Prologue .............................................................................

For every finite n ≥ 4 there is a logically valid sentence φn with the following properties: φn contains only 3 variables (each of which occurs many times); φn contains exactly one nonlogical binary relation symbol (no function symbols, no constants, and no equality symbol); φn has a proof in first-order logic with equality that contains exactly n variables, but no proof containing only n − 1 v...

We construct a family of separable Hilbertian operator spaces, such that the relation of complete isomorphism between the subspaces of each member of this family is complete Kσ . We also investigate some interesting properties of completely unconditional bases of the spaces from this family. In the Banach space setting, we construct a space for which the relation of isometry of subspaces is equ...

ly, we assume there is some function that extracts the angles, size, color, or whatever other property of elements we’re interested in. Two elements would be considered equivalent iff the function extracts the same value for each. � Course Notes, Week 4: Binary Relations 3 For example, if fc is the function mapping a triangle to the lengths its sides, then fc determines the congruence relation....