Searcharxiv⌕ Search

arXiv subjects

Zlatan Damnjanovic

Publications and source records attributed to Zlatan Damnjanovic.

4 recordsLinked to original sources
arXiv2026

Notes on Systems of Very Weak Unary Dyadic Arithmetic

We introduce several very weak first-order theories of unary concatenation of dyadic strings and investigate their relationships to other previously studied veey weak first-order theories, namely the theory WT of binary trees of Kristiansen and Murwanashyaka, the theory WD of binary concatenation of Murwanashyaka, and Robinson's very weak arithmetic R. We prove that all these theories are mutually formally interpretable with the theories of unary concatenation studied in the paper, thus establishing essential undecidability of the latter. In the process we show that binary concatenation is first-order definable from unary concatenation modulo the presence of the initial segment relation plus either the end segment relation or the inverse operation on words, thus giving a positive solution to a problem posed by Karlov.

math.LO↗
arXiv2021

Mutual Interpretability of Weak Essentially Undecidable Theories

Kristiansen and Murwanashyaka recently proved that Robinson arithmetic Q is interpretable in an elementary theory of full binary trees, T. We prove that, conversely, T is interpretable in Q by producing a formal interpretation of T in an elementary concatenation theory, thereby also establishing mutual interpretability of T with several well-known weak essentially undecidable theories of numbers, strings and sets. We also in introduce a "hybrid" elementary theory of strings and trees and establish its mutual interpretability with Robinson's weak arithmetic R, the weak theory of binary trees WT of Kristiansen and Murwanashyaka and a weak concatenation theory of Higuchi and Hirohata.

math.LO↗
arXiv2017

From Strings to Sets

A complete proof is given of relative interpretability of Adjunctive Set Theory with Extensionality in an elementary concatenation theory.

math.LO↗