Tree Theory: Interpretability Between Weak First-Order Theories of Trees

Bulletin of Symbolic Logic 29 (4):465-502 (2023)
  Copy   BIBTEX

Abstract

Elementary first-order theories of trees allowing at most, exactly $\mathrm{m}$, and any finite number of immediate descendants are introduced and proved mutually interpretable among themselves and with Robinson arithmetic, Adjunctive Set Theory with Extensionality and other well-known weak theories of numbers, sets, and strings.

Categories

Keywords

Reprint years

DOI

10.1017/bsl.2023.5

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 106,169

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

Mutual Interpretability of Weak Essentially Undecidable Theories.Zlatan Damnjanovic - 2022 - Journal of Symbolic Logic 87 (4):1374-1395.
Mutual interpretability of Robinson arithmetic and adjunctive set theory with extensionality.Zlatan Damnjanovic - 2017 - Bulletin of Symbolic Logic 23 (4):381-404.
Arithmetic on semigroups.Mihai Ganea - 2009 - Journal of Symbolic Logic 74 (1):265-278.
On Interpretability in the Theory of Concatenation.Vítězslav Švejdar - 2009 - Notre Dame Journal of Formal Logic 50 (1):87-95.
Minimal truth and interpretability.Martin Fischer - 2009 - Review of Symbolic Logic 2 (4):799-815.
Weak Theories of Concatenation and Arithmetic.Yoshihiro Horihata - 2012 - Notre Dame Journal of Formal Logic 53 (2):203-222.
Peano Corto and Peano Basso: A Study of Local Induction in the Context of Weak Theories.Albert Visser - 2014 - Mathematical Logic Quarterly 60 (1-2):92-117.
On interpretations of bounded arithmetic and bounded set theory.Richard Pettigrew - 2009 - Notre Dame Journal of Formal Logic 50 (2):141-152.
First-order theories of bounded trees.Ruaan Kellerman - 2021 - Archive for Mathematical Logic 61 (1):263-297.
A feasible theory for analysis.Fernando Ferreira - 1994 - Journal of Symbolic Logic 59 (3):1001-1011.

Analytics

Added to PP
2023-02-12

Downloads
42 (#593,768)

6 months
9 (#445,453)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Zlatan Damnjanovic
University of Southern California

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references