Results 21 to 30 of about 86 (68)

Interpretations over Heyting's Arithmetic

open access: yes, 1995
In this paper we experiment with a rather general notion of “interpretation in constructive arithmetical theories”. We prove a number of elementary properties of the notion introduced. We prove a number of negative results for interpretations that commute with disjunction. These negative results diverge markedly from what is known in the classical case.
openaire   +1 more source

The Role of the Mizar Mathematical Library for Interactive Proof Development in Mizar. [PDF]

open access: yesJ Autom Reason, 2018
Bancerek G   +6 more
europepmc   +1 more source

Propositional combinations of Σ-sentences in Heyting's Arithmetic

open access: yes, 1994
This paper is mainly about Boolean combinations of Σ-formulas (B(Σ)-formulas) in HA. We prove a theorem guaranteeing that if a B(Σ)-formula is provable in HA, then a simpler one is also provable. Our theorem yields a characterization of the derived rules of HA for Σ-substitutions.
openaire   +1 more source

Intuitionism, Kripke’s Schema, Second-order Heyting arithmetic, Intuitionistic Real algebra, Interpretation

open access: yes
We show that in the presence of a strengthened Kripke’s schema — a plausible addition to the axiomatisation of intuitionistic analysis (see in e.g. [1] or [2]) — choice sequences can be recursively encoded in intuitionistic real algebra. Choice sequences are intuitionistically meaningful counterparts of sequences of natural numbers, and with them ...
openaire   +1 more source

Home - About - Disclaimer - Privacy