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- Maria Emilia Maietti
- Ann. Pure Appl. Logic
- 2009

We present a two-level theory to formalize constructive mathematics as advocated in a previous paper with G. Sambin [MS05]. One level is given by an intensional type theory, called Minimal type theory. This theory extends the set-theoretic version introduced in [MS05] with collections. The other level is given by an extensional set theory that is… (More)

We extend the notion of exact completion on a category with weak finite limits to Lawvere’s elementary doctrines. We show how any such doctrine admits an elementary quotient completion, which is the universal solution to adding certain quotients. We note that the elementary quotient completion can be obtained as the composite of two other universal… (More)

- Maria Emilia Maietti, Silvio Valentini
- J. Symb. Log.
- 2004

- Maria Emilia Maietti, Paola Maneggia, Valeria de Paiva, Eike Ritter
- Applied Categorical Structures
- 2005

There are several kinds of linear typed calculus in the literature, some with their associated notion of categorical model. Our aim in this paper is to systematise the relationship between three of these linear typed calculi and their models. We point out that mere soundness and completeness of a linear typed calculus with respect to a class of categorical… (More)

- GIANLUIGI BELLIN, Stefano Berardi, +6 authors Edmund Robinson
- 2006

We study the proof-theory of co-Heyting algebras and present a calculus of continuations typed in the disjunctive–subtractive fragment of dual intuitionistic logic. We give a single-assumption multiple-conclusions Natural Deduction system NJ for this logic: unlike the best-known treatments of multiple-conclusion systems (e.g., Parigot’s λ−μ calculus, or… (More)

Suppose in an arithmetic unverse we have two predicates φ and ψ for natural numbers, satisfying a base case φ(0) → ψ(0) and an induction step that, for generic n, the hypothesis φ(n) → ψ(n) allows one to deduce φ(n+ 1) → ψ(n+ 1). Then it is already true in that arithmetic universe that (∀n)(φ(n) → ψ(n)). This is substantially harder than in a topos, where… (More)

- Maria Emilia Maietti, Silvio Valentini
- Math. Log. Q.
- 1999

In this paper we analyze an extension of Martin-Löf’s intensional set theory by means of a set contructor P such that the elements of P(S) are the subsets of the set S. Since it seems natural to require some kind of extensionality on the equality among subsets, it turns out that such an extension cannot be constructive. In fact we will prove that this… (More)

- Maria Emilia Maietti
- TYPES
- 1998

We extend Martin-Löf’s constructive set theory with effective quotient sets and the rule of uniqueness of propositional equality proofs. We prove that in the presence of at least two universes U0 and U1 the principle of excluded middle holds for small sets. The key point is the combination of uniqueness of propositional equality proofs with the… (More)

- Maria Emilia Maietti
- Mathematical Structures in Computer Science
- 2005