Syntax for Semantics: Krull’s Maximal Ideal Theorem

&
In Gerhard Heinzmann & Gereon Wolters (eds.), Paul Lorenzen -- Mathematician and Logician. Springer Verlag. pp. 77-102 (2021)
  Copy   BIBTEX

Abstract

Krull’s Maximal Ideal Theorem is one of the most prominent incarnations of the Axiom of Choice in ring theory. For many a consequence of AC, constructive counterparts are well within reach, provided attention is turned to the syntactical underpinning of the problem at hand. This is one of the viewpoints of the revised Hilbert Programme in commutative algebra, which will here be carried out for MIT and several related classical principles.

Categories

Add categories

Keywords

Reprint years

DOI

10.1007/978-3-030-65824-3_6

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,150

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

A New Proof that “Krull implies Zorn”.Bernhard Banaschewski - 1994 - Mathematical Logic Quarterly 40 (4):478-480.
The axiom of choice holds iff maximal closed filters exist.Horst Herrlich - 2003 - Mathematical Logic Quarterly 49 (3):323.
The maximal linear extension theorem in second order arithmetic.Alberto Marcone & Richard A. Shore - 2011 - Archive for Mathematical Logic 50 (5-6):543-564.
Krull dimension in modal logic.Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan & Jan van Mill - 2017 - Journal of Symbolic Logic 82 (4):1356-1386.
Lorenzen’s Reshaping of Krull’s Fundamentalsatz for Integral Domains.Stefan Neuwirth - 2021 - In Gerhard Heinzmann & Gereon Wolters (eds.), Paul Lorenzen -- Mathematician and Logician. Springer Verlag. pp. 143-183.
Maximal chains in the fundamental order.Steven Buechler - 1986 - Journal of Symbolic Logic 51 (2):323-326.
Maximal Possibilities.David Sanson - manuscript
Ideal generalizations of Egoroff’s theorem.Miroslav Repický - 2020 - Archive for Mathematical Logic 59 (7-8):957-977.
A geometric form of the axiom of choice.J. L. Bell - unknown
Maximal irredundance and maximal ideal independence in Boolean algebras.J. Donald Monk - 2008 - Journal of Symbolic Logic 73 (1):261-275.
${\Cal d}$-maximal sets.Peter A. Cholak, Peter Gerdes & Karen Lange - 2015 - Journal of Symbolic Logic 80 (4):1182-1210.
-Maximal sets.Peter A. Cholak, Peter Gerdes & Karen Lange - 2015 - Journal of Symbolic Logic 80 (4):1182-1210.
Ideal convergence of bounded sequences.Rafał Filipów, Recław Ireneusz, Mrożek Nikodem & Szuca Piotr - 2007 - Journal of Symbolic Logic 72 (2):501-512.
Hechler’s theorem for the null ideal.Maxim R. Burke & Masaru Kada - 2004 - Archive for Mathematical Logic 43 (5):703-722.
A co-analytic maximal set of orthogonal measures.Vera Fischer & Asger Törnquist - 2010 - Journal of Symbolic Logic 75 (4):1403-1414.

Analytics

Added to PP
2022-03-10

Downloads
2 (#1,806,630)

6 months
2 (#1,203,746)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Peter Schuster
University of Leeds

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references