Local definability theory

Some local definability theory for holomorphic functions

Let F be a collection of holomorphic functions and let R(PR(F)) denote the reduct of the structure Ran to the ordered field operations together with the set of proper restrictions (see below) of the real and imaginary parts of all functions in F . We ask the question: Which holomorphic functions are locally definable (ie have their real and imaginary parts locally definable) in the structure R(...

Definability in the local theory of the ω-enumeration degrees

We continue the study of the local theory of the structure of the ω-enumeration degrees, started by Soskov and Ganchev [7]. We show that the classes of 1-high and 1-low ω-enumeration degrees are definable. We prove that a standard model of arithmetic is definable as well. 1 ω-enumeration degrees In computability theory there is a vast variety of reducibility relations. Informally, the common fe...

Definability and global degree theory

Gödel’s work [Gö34] on undecidable theories and the subsequent formalisations of the notion of a recursive function ([Tu36], [Kl36] etc.) have led to an ever deepening understanding of the nature of the non-computable universe (which as Gödel himself showed, includes sets and functions of everyday significance). The nontrivial aspect of Church’s Thesis (any function not contained within one of ...

Definability in Logic and Rough Set Theory

Rough set theory is an effective tool for data mining. According to the theory, a concept is definable if it can be written as a Boolean combination of equivalence classes induced from classification attributes. On the other hand, definability in logic has been explicated by Beth’s theorem. In this paper, we propose two data representation formalisms, called first-order data logic (FODL) and at...

Definability in the Monadic Second-Order Theory of Successor