February 2023 Core Gödel
Neil Tennant
Author Affiliations +
Notre Dame J. Formal Logic 64(1): 15-59 (February 2023). DOI: 10.1215/00294527-2022-0033

Abstract

This study examines how the Gödel phenomena are to be treated in core logic. We show in formal detail how one can use core logic in the metalanguage to prove Gödel’s incompleteness theorems for arithmetic even when classical logic is used for logical closure in the object language.

Dedication

In memoriam Mic Detlefsen

Citation

Download Citation

Neil Tennant. "Core Gödel." Notre Dame J. Formal Logic 64 (1) 15 - 59, February 2023. https://doi.org/10.1215/00294527-2022-0033

Information

Received: 11 June 2021; Accepted: 12 September 2022; Published: February 2023
First available in Project Euclid: 23 March 2023

MathSciNet: MR4564835
zbMATH: 07690432
Digital Object Identifier: 10.1215/00294527-2022-0033

Subjects:
Primary: 03F30
Secondary: 03B47 , 03F40 , 03F52 , 03F99

Keywords: 1-consistency , classical core logic , consistency , core logic , ex falso quodlibet , Gödel phenomena , Incompleteness , recursive functions , representability , ω-consistency

Rights: Copyright © 2023 University of Notre Dame

Vol.64 • No. 1 • February 2023
Back to Top