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

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 class… Expand

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 definable… Expand

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 settles… Expand

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

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

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 of… Expand

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

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