Inaccessibility in constructive set theory and type theory

Inaccessibility in Constructive Set Theory and Type Theory

This paper is the rst in a series whose objective is to study notions of large sets in the context of formal theories of constructivity. The two theories considered are Aczel's constructive set theory (CZF) and Martin-LL of's intuitionistic theory of types. This paper treats Mahlo's-numbers which give rise classically to the enumer-ations of inaccessibles of all transsnite orders. We extend the...

Quotient topologies in constructive set theory and type theory

The standard construction of quotient spaces in topology uses full separation and power sets. We show how to make this construction using only the (generalised) predicative methods available in constructive type theory and constructive set theory. MSC: primary 03F65, 54B15, secondary 03B15, 03E70.

Elementary Constructive Operational Set Theory

We introduce an operational set theory in the style of [5] and [17]. The theory we develop here is a theory of constructive sets and operations. One motivation behind constructive operational set theory is to merge a constructive notion of set ([1], [2]) with some aspects which are typical of explicit mathematics [14]. In particular, one has non-extensional operations (or rules) alongside exten...

Notes on Constructive Set Theory

4 Operations on Sets and Classes 25 4.1 Class Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2 Class Relations and Functions . . . . . . . . . . . . . . . . . . 26 4.3 Some Consequences of Union-Replacement . . . . . . . . . . . 27 4.4 Russell’s paradox . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.5 Subset Collection and Exponentiation . . . . . . . . . . . . . . 30...

A More General Type Theoretic Interpretation Of Constructive Set Theory