PAI Private Arithmetics Institute       

Natural Numbers, Recursion, Geometry, Symmetry, Axioms, Logic, Metalanguage and more 


There is more to come

In the adjacent publications use is made of the systematic as it is indicated on page Home . A survey on the current work on 'Opus logico-mathematicus' is shown at the right-hand table. It will give in detail the description of object-language Funcish and metalanguage Mencish, as well as the logical rules obeying correct metalingual treatment. Furthermore it will introduce three kind of concrete calcules relating to natural numbers and recursion:

ALPHA          simple arithmetic functions

                       (essentially Robinson arithmetic)

NU                  recursive functions by programming for the FAGATOR calculator

                       (update of Church-publication of 2006)

LAMBDA       direct introduction of recursive functions by the PINITOR calculator

                       (primitive recursive functions and beyond)

In separate publications there will be abstract calcules too, e.g. :

rho                rational number arithmetic (first-order logic)

deltaalpha   biradical number arithmetic (first-order logic)

delta             algebraical number arithmetic (first-order logic)

eta                biderivational number arithmetic (second-order logic)

zeta              real number arithmetic (third-order logic)