Set Theoretic Real Analysis

Set Theoretic Real Analysis

This article is a survey of the recent results that concern real functions (from R into R) and whose solutions or statements involve the use of set theory. The choice of the topics follows the author’s personal interest in the subject, and there are probably some important results in this area that did not make it to this survey. Most of the results presented here are left without proofs. 1991 ...

On some problems in set-theoretic real analysis

This thesis contains a few applications of set-theoretic methods to certain problems in real analysis. In the first two sections of Chapter 1, we discuss some results related to a question of Fremlin about partitions of a set of reals into null sets. In Section 3, we answer a question of Komjáth in dimension one. Our proof uses some results of Gitik and Shelah in an essential way. There seems t...

Set-theoretic Analysis of Nominative Data

In the paper we investigate the notion of nominative data that can be considered as a general mathematical model of data used in computing systems. The main attention is paid to flat nominative data called nominative sets. The structure of the partially-ordered set of nominative sets is investigated in terms of set theory, lattice theory, and algebraic systems theory. To achieve this aim the co...

The Set Theoretic Structure of Analysis

A Set-Theoretic Model for Real-Time Specification and Reasoning

Timed-trace formalisms have emerged as a powerful method for specifying and reasoning about concurrent real-time systems. We present a simple variant which builds methodically on set theory, and is thus suitable for use by programmers with little formal methods experience.