Weierstrass's final theorem of arithmetic is not final.

The Recursion Theorem (final)

Kleene’s Recursion Theorem, though provable in only a few lines, is fundamental to computability theory and allows strong self-reference in proofs. It is a fixed-point theorem in the sense that it asserts for any total computable function f , there is a number n such that n and f(n) index (or code) the same partial computable function (though we need not have f(n) = n). In this paper we will pr...

?Logic and Formal Ontology: Is the Final Formal Ontology Possible

Musa Akrami AbstractMany philosophers and logicians have contemplated the relationship between ontology and logic. The author of this paper, working within a Bolzanoan-Husserlian tradition of studying both ontology and logic, considers ontology as the science of the most general features of beings and the most general relations among them. He considers logic as the science concernin...

A small final coalgebra theorem

This paper presents an elementary and self-contained proof of an existence theorem of nal coalgebras for endofunctors on the category of sets and functions.

Final booklet

Dirichlet’s Theorem on Primes in Arithmetic Sequences Math 129 Final Paper

Dirichlet’s theorem on primes in arithmetic sequences states that in any arithmetic progression m,m + k, m + 2k, m + 3k, . . ., there are infinitely many primes, provided that (m, k) = 1. Euler first conjectured a result of this form, claiming that every arithmetic progression beginning with 1 contained an infinitude of primes. The theorem as stated was conjectured by Gauss, and proved by Diric...