Abstract Following the Kronecker–Duval or D5 philosophy of dynamic evaluation in
computer algebra, the dynamical proof method was brought into constructive algebra in …

The existence of a maximal ideal in a general nontrivial commutative ring is tied together
with the axiom of choice. Following Berardi, Valentini and thus Krivine but using the relative …

We introduce a general notion of flabby objects in elementary toposes and study their basic
properties. In the special case of localic toposes, this notion reduces to the common notion …

Toposes can be pictured as mathematical universes. Besides the standard topos, in which
most of mathematics unfolds, there is a colorful host of alternate toposes in which …

The purpose of this contribution is to give a coherent account of a particular narrative which
links locales, geometric theories, sheaf semantics and constructive commutative algebra …

The existence of a maximal ideal in a general nontrivial commutative ring is tied together
with the axiom of choice. Following Berardi, Valentini and thus Krivine but using the relative …

§1. Introduction. 1.1. What predicativism, and why? In [44] the basic historic problem of the
research in foundations of mathem Page 1 The Bulletin of Symbolic Logic Volume 30, Number …

(*) What are we implicitly committed to in accepting a theory S and what can we justifiably
accept? As is well-known,(*) has its roots in the work by Kreisel (1958), Kreisel (1970). 2 Our …

The topic of this thesis lies in the intersection between proof theory and algebraic logic. The
main object of discussion, constructive reasoning, was introduced at the beginning of the …

Let us assume that Sentence A is true. Then, by definition, the Eiffel Tower is located in
Munich. Discharging the assumption, we can state that “If Sentence A is true, then the Eiffel …