Axiomatizations of arithmetic and the first-order/second-order divide

efl students gender and socioeconomic status: the use of politeness strategies in the first and second languages

within the components of communicative competence, a special emphasis is put on the “rules of politeness,” specifically the politeness strategies (brown and levinson, 1978) that speakers deploy when performing the request speech act. this is because the degree of imposition that making a request places upon one’s interlocutor(s) has been seen to be influenced by several factors among which, as ...

First-Order Proof Theory of Arithmetic

The First Geometric–Arithmetic Index of Some Nanostar Dendrimers

Dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core [1,4]. These are key molecules in nanotechnology and can be put to good use. In this article, we compute the first geometricarithmetic index of two infinite classes of dendrimers.

Π1-ordinal analysis beyond first-order arithmetic

In this paper we give an overview of an essential part of a Π1 ordinal analysis of Peano Arithmetic (PA) as presented by Beklemishev ([2]). This analysis is mainly performed within the polymodal provability logic GLPω. We reflect on ways of extending this analysis beyond PA. A main difficulty in this is to find proper generalizations of the so-called Reduction Property. The Reduction Property r...

Axiomatizations and Conservation Results for Fragments of Bounded Arithmetic

This paper presents new results on axiomatizations for fragments of Bounded Arithmetic which improve upon the author’s dissertation. It is shown that (Σi+1 ∩Π b i+1)-PIND and strong Σ b i -replacement are consequences of S 2 . Also ∆ b i+1 -IND is a consequence of T i 2 . The latter result is proved by showing that S 2 is ∀∃Σ b i+1 -conservative over T i 2 . Furthermore, S i+1 2 is conservative...