Nonstandard definability

Delta1-Definability

Boban Veli ckovi c y Jensen's Coding Theorem provides a method for making a class of ordinals 2-deenable in a real. In this paper we explore the possibility of obtaining a 1-deenition. While this is not possible in general, we show that by assuming enough condensation, a class can be made 1 in a real parameter in a class-generic extension. Our main application is the following. Theorem There is...

FOUNDATIONS OF NONSTANDARD ANALYSIS A Gentle Introduction to Nonstandard Extensions

Nonstandard Analysis in Topology: Nonstandard and Standard Compactifications

Let (X,T ) be a topological space, and X a non–standard extension of X . There is a natural “standard” topology T on X generated by G, where G ∈ T . The topological space ( X, T ) will be used to study, in a systematic way, compactifications of (X,T ) . Mathematics Subject Classification: 031105, 54J05, 54D35, 54D60.

Naturality and Definability Ii

In two papers [3] and [4] we noted that in common practice many algebraic constructions are defined only ‘up to isomorphism’ rather than explicitly. We mentioned some questions raised by this fact, and we gave some partial answers. The present paper provides much fuller answers, though some questions remain open. Our main result, Theorem 4, says that there is a transitive model of Zermelo-Fraen...

Definability and Full Abstraction

Game semantics has renewed denotational semantics. It offers among other things an attractive classification of programming features, and has brought a bunch of new definability results. In parallel, in the denotational semantics of proof theory, several full completeness results have been shown since the early nineties. In this note, we review the relation between definability and full abstrac...