 Author
 Year
 2014
 Title
 Sort logic and foundations of mathematics
 Event
 Workshop on Infinity and Truth (Singapore)
 Book/source title
 Infinity and truth
 Pages (fromto)
 171186
 Publisher
 Singapore: World Scientific
 ISBN
 9789814571036
 ISBN (electronic)
 9789814571050
9789814571043  Serie
 Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore: 17930758
 Volume (Serie)
 25
 Document type
 Conference contribution
 Faculty
 Interfacultary Research Institutes
 Institute
 Institute for Logic, Language and Computation (ILLC)
 Abstract

I have argued elsewhere [8] that second order logic provides a foundation for mathematics much in the same way as set theory does, despite the fact that the former is second order and the latter first order, but second order logic is marred by reliance on ad hoc large domain assumptions. In this chapter I argue that sort logic, a powerful extension of second order logic, provides a foundation for mathematics without any ad hoc large domain assumptions. The large domain assumptions are replaced by ZFClike axioms. Despite this resemblance to set theory sort logic retains the structuralist approach to mathematics characteristic of second order logic. As a modeltheoretic logic sort logic is the strongest logic. In fact, every model class definable in set theory is the class of models of a sentence of sort logic. Because of its strength sort logic can be used to formulate particularly strong reflection principles in set theory.
 URL
 go to publisher's site
 Language
 English
 Permalink
 http://hdl.handle.net/11245/1.406590
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