Fast-Collapsing Theories

Studia Logica 103 (1):53-73 (2015)
  Copy   BIBTEX

Abstract

Reinhardt’s conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite induction just beyond the first epsilon number. We prove a weaker version of the conjecture, by elementary methods and transfinite induction up to a smaller ordinal.

Other Versions

original Alexander, Samuel A. (2013) "Fast-Collapsing Theories". Studia Logica 1():1-21

Links

PhilArchive

External links

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

Through your library

Similar books and articles

A Machine That Knows Its Own Code.Samuel A. Alexander - 2014 - Studia Logica 102 (3):567-576.
Ordinal analyses for monotone and cofinal transfinite inductions.Kentaro Sato - 2020 - Archive for Mathematical Logic 59 (3-4):277-291.
Transfinite Induction.Henryk Kotlarski - 2019 - In A Model–Theoretic Approach to Proof Theory. Cham, Switzerland: Springer Verlag. pp. 73-87.
Intuitionistically provable recursive well-orderings.Harvey M. Friedman & Andre Scedrov - 1986 - Annals of Pure and Applied Logic 30 (2):165-171.
Fraïssé’s conjecture in [math]-comprehension.Antonio Montalbán - 2017 - Journal of Mathematical Logic 17 (2):1750006.
Transfinite induction within Peano arithmetic.Richard Sommer - 1995 - Annals of Pure and Applied Logic 76 (3):231-289.
Weak Well Orders and Fraïssé’s Conjecture.Anton Freund & Davide Manca - forthcoming - Journal of Symbolic Logic:1-16.
Epsilon substitution for transfinite induction.Henry Towsner - 2005 - Archive for Mathematical Logic 44 (4):397-412.
On the restricted ordinal theorem.R. L. Goodstein - 1944 - Journal of Symbolic Logic 9 (2):33-41.

Analytics

Added to PP
2025-06-17

Downloads
14 (#1,970,849)

6 months
3 (#1,866,497)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Samuel Allen Alexander
Ohio State University (PhD)

References found in this work

Minds, Machines and Gödel.J. R. Lucas - 1961 - Etica E Politica 5 (1):1.
God, the Devil, and Gödel.Paul Benacerraf - 1967 - The Monist 51 (1):9-32.
A Machine That Knows Its Own Code.Samuel A. Alexander - 2014 - Studia Logica 102 (3):567-576.
Self-referential theories.Samuel A. Alexander - 2020 - Journal of Symbolic Logic 85 (4):1687-1716.

View all 7 references / Add more references