RELATIVE DEFINABILITY OF n-GENERICS

Relative Definability in Formal Ontologies

The paper investigates technical meta-logical notions and theorems relating to definitions and relative definability and shows how these are relevant to the concerns of knowledge representation. In particular they can be used to identify sets of primitives that are sufficent to fully describe a given domain. Fundamental definability theorems of Tarski are examined, and it is shown how these can...

Relative Definability and Models of Unary PCF

Relative definability of boolean functions via hypergraphs

The aim of this work is to show how hypergraphs can be used as a systematic tool in the classi!cation of continuous boolean functions according to their degree of parallelism. Intuitively f is “less parallel” than g if it can be de!ned by a sequential program using g as its only free variable. It turns out that the poset induced by this preorder is (as for the degrees of recursion) a sup-semila...

Investigations on Relative Definability in Pcf

The focus of this thesis is the study of relative definability of first-order boolean functions with respect to the language PCF, a paradigmatic typed, higher-order language based on the simply-typed λ-calculus. The basic core language is sequential. We study the effect of adding construct that embody various notions of parallel execution. The resulting set of equivalence classes with respect t...

Relative decidability and definability in henselian valued fields

Let (K, v) be a henselian valued field of characteristic 0. Then K admits a definable partition on each piece of which the leading term of a polynomial in one variable can be computed as a definable function of the leading term of a linear map. The main step in obtaining this partition is an answer to the question, given a polynomial f(x) ∈ K[x], what is v(f(x))? Two applications are given: fir...