Our goal is to answer a question proposed by Richard Heck in the paper “Formal Arithmetic Before Grundgesetze”. inquires as reasons why it took almost eight years for Frege honor his promises of concluding project grounding mathematics logic. Although gave some answers, we think that more adequate philosophical discussion can still be offered. This will try fill gap presenting what understand w...

In this paper we investigate the problem of secure instantiation of the random oracle, based on the concepts and methods of algorithmic randomness. We show that, for any secure signature scheme in the random oracle model, there exists a specific computable function which can instantiate the random oracle while keeping the security originally proved in the random oracle model. Our results use th...

If what is known need not be closed under logical consequence, then a distinction arises between something’s being known to be the case (by a specific agent) and its following from something known (to that subject). When each of these notions is represented by a sentence operator, we get a bimodal logic in which to explore the relations between the two notions.