The role played by real-valued functions in functional analysis is fundamental. One often considers metrics, or seminorms, or linear functionals, to mention some important examples. We introduce the notion of deenable real-valued function in functional analysis: a real-valued function f deened on a structure of functional analysis is deenable if it can be \approximated" by formulas which do not...

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To prove the conjecture for this case we observe that if K 0 is FOL{deenable with equality only, then L = INV K0 (L) by proposition 5, and hence EV EN is not K 0-invariantly LFP-deenable. Hence we have Corollary 26. If K 0 is f-categorical and closed under substructures and L 6 = INV K0 (L) then a linear order is deenable with parameters on K 0. In particular , this is the case if EV EN 2 INV K...

The classical simulation of physical processes using standard models of computation is fraught with problems. On the other hand, attempts at modelling real-world computation with the aim of isolating its hypercomputational content have struggled to convince. We argue that a better basic understanding can be achieved through computability theoretic deconstruction of those physical phenomena most...

We consider implicit definability over the natural number system N,+,×,=. We present a new proof of two theorems of Leo Harrington. The first theorem says that there exist implicitly definable subsets of N which are not explicitly definable from each other. The second theorem says that there exists a subset of N which is not implicitly definable but belongs to a countable, explicitly definable ...

We examine a certain modal consequence relation, and define the notion of validity of a modal sequent on a frame. We demonstrate that it is possible to define classes of frames. not definable by modal formulas, by modal sequents. Through the use of modal algebras and general frames, we obtain a characterization of modal sequent-definable classes of frames which are also first-order definable, a...

We look at intensionality from the perspective of computation. In particular, we review how game semantics has been used to characterize the sequential functional processes, leading to powerful and flexible methods for constructing fully abstract models of programming languages, with applications in program analysis and verification. In a broader context, we can regard game semantics as a first...

Ellipses are a meta-linguistic notation for denoting terms the size of which are specified by a meta-variable that ranges over the natural numbers. In this work, we present a systematic approach for encoding such meta-expressions in the λ-calculus, without ellipses: Terms that are parameterized by meta-variables are replaced with corresponding λ-abstractions over actual variables. We call such ...

We consider the definability of mad families in vector spaces form ⨁ n < ω F where is a field cardinality ≤ ℵ 0 . show that there no analytic family subspaces when = 2 , partially answering question Smythe. Our proof relies on variant Mathias forcing restricted to certain idempotent ultrafilter whose existence follows from Glazer's Hindman's theorem.

We investigate the defining power of stratified and hierarchical logic programs. As an example for the treatment of negative information in the context of these structured programs we also introduce a stratified and hierarchical closed-world assumption. Our analysis tries to relate the defining power of stratified and hierarchical programs (with and without an appropriate closed-world assumptio...