Noncomparabilities & Nonstandard Logics

Nonstandard methods in many-valued logics

Since MV-algebras include, in an essential way, infinitisimals it was felt that a systematic study of relationships of nonstandard methods and MV-algebras was needed. In this paper we try to introduce some basic frameworks to study MV-algebras from a nonstandard point of view. Also one can see that for a complete study of MV-algebras many external objects need to be treated differently.

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.

EQ-logics with delta connective

In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...

Working with Nonstandard Models

Most of the research in foundations of mathematics that I do in some way or another involves the use of nonstandard models. I will give a few examples, and indicate what is involved. 1. General algebra and measurable cardinals. An unexpectedly direct connection. 2. Borel selection and higher set theory. A descriptive set theoretic context extensively pursued by some functional analysts. 3. Equa...