Higher set theory and mathematical practice

Set Theory and Higher-Order Logic: Foundational Issues and Mathematical Developments Program and Practical Information Contents

In 1990, W. Hugh Woodin introduced Omega-logic as an approach to truth in the universe of all sets inspired by recent work on large cardinals and determinacy. In Omega-logic statements are valid if, roughly, they hold in every forcing extension of the universe, or its sufficiently rich initial segments. Thus, Omega-logic is the logic of generic absoluteness. In this short course we will start w...

Implementing Mathematical Objects in Set Theory

In general little thought is given to the general question of how to implement mathematical objects in set theory. It is clear that—at various times in the past—people have gone to considerable lengths to devise implementations with nice properties. There is a literature on the evolution of the Wiener-Kuratowski ordered pair, and a discussion by Quine of the merits of an ordered-pair implementa...

Set Theory, Higher Order Logic or Both?

The majority of general purpose mechanised proof assistants support versions of typed higher order logic, even though set theory is the standard foundation for mathematics. For many applications higher order logic works well and provides, for speciication, the beneets of type-checking that are well-known in programming. However, there are areas where types get in the way or seem unmotivated. Fu...

The Interpretation of Set Theory in Mathematical Predication Theory

FUZZY SOFT SET THEORY AND ITS APPLICATIONS

In this work, we define a fuzzy soft set theory and its related properties. We then define fuzzy soft aggregation operator that allows constructing more efficient decision making method. Finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties.