We define and elaborate upon the notion of computable reducibility between equivalence relations on the natural numbers, providing a natural computable analogue of Borel reducibility, and investigate the hierarchy to which it gives rise. The theory appears well suited for an analysis of equivalence relations on classes of c.e. structures, a rich context with many natural examples, such as the i...

Frege’s Grundgesetze der Arithmetik is formally inconsistent. This system is essentially second-order logic together with an abstraction operator that abides to Frege’s Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the Grundgesetze is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for con...

The theory of self-testing/correcting programs by random self-reducibility (RSR) [1, 2, 5] is a novel and powerful tool to approach the problem of program correction. It allows real-time testing and correcting of programs. Moreover, it allows the simultaneous checking of the hardware and software without requiring any knowledge of the implementation of a program. Basically, a function is random...

Let H be a reductive subgroup of a reductive group G over an algebraically closed field k. We consider the action of H on Gn, the n-fold Cartesian product of G with itself, by simultaneous conjugation. We give a purely algebraic characterization of the closed H-orbits in Gn, generalizing work of Richardson which treats the case H = G. This characterization turns out to be a natural generalizati...

Many NP-complete problems have counting versions which are #P-complete. On the other hand, #Perfect Matchings is also Cook-complete for #P, which is surprising as Perfect Matching is actually in P (which implies that #Perfect Matchings cannot be Karp-complete for #P). Here, we study the complexity class #PE (functions of #P with easy decision version). The inclusion #PE ⊆ #P is proper unless P ...

We prove a reducibility result for $sl(2,\mathbb {R})$ quasi-periodic cocycles close to constant elliptic matrix in ultra-differentiable classes, under an adapted arithmetic condition which extends the Brjuno-Rüssmann analytic case. The proof is based on elementary property of fibered rotation number and deals with functions weighted Fourier norm. also show that weaker necessary reducibility, ...

Although original, intricate and sophisticated, Gregg Rosenberg’s core argument in favor of panpsychism is a version of an argument that has been around for some time. My paper tries to shed some light on Rosenberg's strategy by comparing it to the views of Leibniz (or a fictional philosopher close to him) who took a similar approach. At the heart of the argument is the idea that relational pro...

All the posets/lattices considered here are finite with element 0. An element x of a poset satisfying certain properties is deletable if P − x is a poset satisfying the same properties. A class of posets is reducible if each poset of this class admits at least one deletable element. When restricted to lattices, a class of lattices is reducible if and only if one can go from any lattice in this ...