PhilSci Archive

Completeness and Categoricity, Part I: 19th Century Axiomatics to 20th Century Metalogic

Awodey, Steve and Reck, Erich H. (2002) Completeness and Categoricity, Part I: 19th Century Axiomatics to 20th Century Metalogic. [Preprint]

[img]
Preview
PDF
ccI.pdf

Download (325kB)
[img]
Preview
Postscript
ccI.ps

Download (292kB)

Abstract

This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics so as to shed new light on the relevant strengths and limits of higher-order logic.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Preprint
Creators:
CreatorsEmailORCID
Awodey, Steve
Reck, Erich H.
Keywords: axiomatic method
Subjects: Specific Sciences > Mathematics
Depositing User: Steve Awodey
Date Deposited: 23 Jan 2002
Last Modified: 07 Oct 2010 15:10
Item ID: 544
URI: http://philsci-archive.pitt.edu/id/eprint/544

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item