5 citations · 8 across the 7 of their papers we have counts for
7 papers · 1 filter
Randomising Realisability
Merlin Carl, Lorenzo Galeotti, Robert Passmann
We consider a randomised version of Kleene's realisability interpretation of intuitionistic arithmetic in which computability is replaced with randomised computability with positiv…
Automatized Evaluation of Formalization Exercises in Mathematics
Merlin Carl
We describe two systems for supporting beginner students in acquiring basic skills in expressing statements in the formalism of first-order predicate logic; the first, called "math…
Number Theory and Axiomatic Geometry in the Diproche System
Merlin Carl
Diproche ("Didactical Proof Checking") is an automatic system for supporting the acquistion of elementary proving skills in the initial phase of university education in mathematics…
Resetting Infinite Time Blum-Shub-Smale-Machines
Merlin Carl, Lorenzo Galeotti
In this paper, we study strengthenings of Infinite Times Blum-Shub-Smale-Machines (ITBMs) that were proposed by Seyfferth in [14] and Welch in [15] obtained by modifying the behavi…
A transfer principle for second-order arithmetic, and applications
Merlin Carl, Asgar Jamneshan
In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often…
A note on as a direct summand of nonstandard models of weak systems of arithmetic
Merlin Carl
There are nonstandard models of normal open induction () for which is a direct summand of their additive group. We show that this is impossible for nonstandard mo…