• Publications
  • Influence
Automatic Synthesis of Typed Lambda-Programs on Term Algebras
TLDR
The notion of iteratively defined functions from and to heterogeneous term algebras is introduced as the solution of a finite set of equations of a special shape. Expand
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  • 10
Innite -calculus and non-sensible models
We dene a model of -calculus which is similar to the model of Bohm trees, but it does not identify all the unsolvable lambda-terms. The role of the unsolvable terms is taken by a much smaller classExpand
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An additive measure in o-minimal expansions of fields
Given an o-minimal structure M which expands a field, we define, for each positive integer d, a real valued additive measure on a Boolean algebra of subsets of Md and we prove that all the definableExpand
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On the Cop Number of a Graph
The cop number c(G) of a graph G is an invariant connected with the genus and the girth. We prove that for a fixed k there is a polynomial-time algorithm which decides whether c(G) @? k. This settlesExpand
  • 105
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The Interpretability Logic of Peano Arithmetic
  • A. Berarducci
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 1 September 1990
TLDR
We give an axiomatization and a decision procedure for the class of those modal formulas that express valid interpretability principles The relation of interpretability between axiomatic theories (formulated in first order logic) has been used to prove relative consistency results, decidability and undecidability of theories, and to compare the strength of theories. Expand
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A Self-Interpreter of Lambda Calculus Having a Normal Form
TLDR
We formalize a technique introduced by Bohm and Piperno to solve systems of recursive equations in lambda calculus without the use of the fixed point combinator and using only normal forms. Expand
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Factorization in generalized power series
The field of generalized power series with real coefficients and exponents in an ordered abelian divisible group G is a classical tool in the study of real closed fields. We prove the existence ofExpand
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Combinatorial Principles in Elementary Number Theory
TLDR
We prove that the theory IΔ 0 , extended by a weak version of the Δ 0 -Pigeonhole Principle, proves that every integer is the sum of four squares (Lagrange's theorem). Expand
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A descending chain condition for groups definable in o-minimal structures
TLDR
We prove that if G is a group definable in a saturated o-minimal structure, then G has a smallest (necessarily normal) type-definable subgroup G 00 of bounded index and G/G 00 equipped with the “logic topology” is a compact Lie group. Expand
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