We study the classes of hypersimple and semicomputable sets as well as their intersection in the weak truth table degrees. We construct degrees that are not bounded by hypersimple degrees outside any non-trivial upper cone of Turing degrees and show that the hypersimple-free c.e. wtt degrees are downwards dense in the c.e. wtt degrees. We also show that there is no maximal (w.r.t. ≤wtt) hypersimple wtt degree. Moreover, we consider the sets that are both hypersimple and semicomputable, characterize (...) them as the (bi-infinite) c.e. cuts of computable orderings of ℕ of order type ω+ω* and study their wtt degrees. We show that there are hypersimple degrees that are not bounded by any hypersimple semicomputable degree, investigate relationships with the join and look for maximal and minimal elements of related classes. (shrink)

We examine conditions under which, in a computable topological space, a semicomputable set is computable. It is known that in a computable metric space a semicomputable set S is computable if S is a continuum chainable from a to b, where a and b are computable points, or S is a circularly chainable continuum which is not chainable. We prove that this result holds in any computable topological space.

We examine topological pairs (\Delta, \Sigma) which have computable type: if X is a computable topological space and f:\Delta \rightarrow X a topological embedding such that f(\Delta) and f(\Sigma) are semicomputable sets in X, then f(\Delta) is a computable set in X. It it known that (D, W) has computable type, where D is the Warsaw disc and W is the Warsaw circle. In this paper we identify a class of topological pairs which are similar to (D, W) and (...) have computable type: we prove that (\Delta, \Sigma) has computable type if \Delta can somehow be approximated by a 2-cell whose boundary circle approximates \Sigma. Moreover, we examine higher-dimensional analogues of such pairs. (shrink)

Objetivo. Verificar si el procesamiento semántico de estímulos visuales complejos, como la repetición, la identidad, el orden y la doble incongruencia, es recursivo o computable. Sujetos y métodos. Veintisiete universitarios respondieron a un paradigma adaptado N400 con cinco condiciones, cada una con 80 tareas, mientras se registraba su actividad cerebral con un gorro de 64 electrodos. Resultados. Dos ventanas temporales de 400 a 550 ms y de 550 a 800 ms se analizaron mediante un contraste ANOVA del factor condición por (...) regiones de interés. Además, se calculó la solución inversa de las ventanas mediante tomografía electromagnética de baja resolución para identificar las fuentes corticales subyacentes a los potenciales eléctricos. Se corroboran diferencias significativas (p< 0, 05) en los potenciales N400 y P600 en áreas frontales y centroparietales asociadas a los operadores lógicos estudiados. Conclusión. Se confirma que el procesamiento cerebral de imágenes complejas (congruentes/incongruentes) es modulado por la repetición, la identidad y el orden, pero no por la negación. Por consiguiente, se puede decir que el procesamiento semántico de imágenes complejas es semicomputable. (shrink)

We use the theory of domains with totality to construct some logics generalizing ω-logic and β-logic and we prove a completenes theorem for these logics. The key application is E-logic, the logic related to the functional 3E. We prove a compactness theorem for sets of sentences semicomputable in 3E.

We study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described by a computably enumerable set, such as lower semicomputable functions. The corresponding randomness notions are slightly stronger than Martin–Löf randomness.We establish several equivalences. Given a ML-random realz, the additional randomness strengths needed for the following are equivalent.all effectively closed classes containingzhave density 1 atz.all nondecreasing functions with uniformly left-c.e. increments are differentiable atz.zis a Lebesgue point (...) of each lower semicomputable integrable function.We also consider convergence of left-c.e. martingales, and convergence in the sense of Birkhoff’s pointwise ergodic theorem. Lastly, we study randomness notions related to density of${\rm{\Pi }}_n^0$and${\rm{\Sigma }}_1^1$classes at a real. (shrink)

We consider topological pairs,, which have computable type, which means that they have the following property: if X is a computable topological space and a topological imbedding such that and are semicomputable sets in X, then is a computable set in X. It is known, e.g., that has computable type if M is a compact manifold with boundary. In this paper we examine topological spaces called graphs and we show that we can in a natural way associate to each (...) graph G a discrete subspace E so that has computable type. Furthermore, we use this result to conclude that certain noncompact semicomputable graphs in computable metric spaces are computable. (shrink)

It is known that a semicomputable continuum S in a computable topological space can be approximated by a computable subcontinuum by any given precision under condition that S is chainable and decomposable. In this paper we show that decomposability can be replaced by the assumption that S is chainable from a to b, where a is a computable point.