About

Zlatan Damnjanovic is an Associate Professor of Philosophy at USC Dornsife. His research focuses on logic and the philosophy of mathematics. He holds a Ph.D. from Princeton University. His academic interests include logic and the philosophy of mathematics, and he is involved in teaching and research within these areas.

Research topics

• Artificial Intelligence
• Computer Science
• Combinatorics
• Discrete mathematics
• Mathematics
• Pure mathematics

Selected publications

• On elementary theories of weighted and labelled trees

  Journal of Logic and Computation · 2025-12-22

  article1st authorCorresponding

  Abstract We introduce two weak first-order theories of weighted and labelled finite trees, T*† and T*‡, respectively. It is proved that T*† and T*‡ are mutually interpretable with other previously studied elementary theories of ‘undecorated’ finite trees, as well as with Robinson Arithmetic, Q, and a host of other weak first-order theories of numbers, strings, sets and sequences.

  PublisherDOI

• TREE THEORY: INTERPRETABILITY BETWEEN WEAK FIRST-ORDER THEORIES OF TREES

  Bulletin of Symbolic Logic · 2023 · 3 citations

  1st authorCorresponding
  • Computer Science
  • Artificial Intelligence
  • Mathematics

  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.

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• MUTUAL INTERPRETABILITY OF WEAK ESSENTIALLY UNDECIDABLE THEORIES

  Journal of Symbolic Logic · 2022 · 5 citations

  1st authorCorresponding
  • Computer Science
  • Artificial Intelligence
  • Mathematics

  Abstract 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 QT + , thereby also establishing mutual interpretability of T with several well-known weak essentially undecidable theories of numbers, strings, and sets. We also introduce a “hybrid” elementary theory of strings and trees, WQT*, and establish its mutual interpretability with Robinson’s weak arithmetic R, the weak theory of trees WT of Kristiansen and Murwanashyaka, and the weak concatenation theory WTC ε of Higuchi and Horihata.

  PublisherDOI

• Mutual Interpretability of Weak Essentially Undecidable Theories

  arXiv (Cornell University) · 2021-04-15

  preprintOpen access1st authorCorresponding

  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.

  PublisherOA PDFDOI

• Mutual Interpretability of Robinson Arithmetic and Adjunctive Set Theory\n with Extensionality

  arXiv (Cornell University) · 2017-07-11

  preprintOpen access1st authorCorresponding

  An elementary rheory of concatenation is introduced and used to establish\nmutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory,\nthe quantifier-free part of Kirby's finitary set theory, and Adjunctive Set\nTheory, with or without extensionality.\n

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• MUTUAL INTERPRETABILITY OF ROBINSON ARITHMETIC AND ADJUNCTIVE SET THEORY WITH EXTENSIONALITY

  Bulletin of Symbolic Logic · 2017-12-01

  preprintOpen access1st authorCorresponding

  Abstract An elementary theory of concatenation, QT + , is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, quantifier-free part of Kirby’s finitary set theory, and Adjunctive Set Theory, with or without extensionality. The most basic arithmetic and simplest set theory thus turn out to be variants of string theory.

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• From Strings to Sets

  arXiv (Cornell University) · 2017-01-26

  preprintOpen access1st authorCorresponding

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

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• Truth Through Proof: A Formalist Foundation for Mathematics * By ALAN WEIR

  Analysis · 2012-02-16

  article1st authorCorresponding

  Journal Article Truth Through Proof: A Formalist Foundation for MathematicsBy Alan Weir Get access Truth Through Proof: A Formalist Foundation for MathematicsBy Alan Weir Oxford University Press, 2010. xiv + 282 pp. £35.00. Zlatan Damnjanovic Zlatan Damnjanovic University of Southern California University Park, Los Angeles CA 90089, USA zlatan@usc.edu Search for other works by this author on: Oxford Academic Google Scholar Analysis, Volume 72, Issue 2, April 2012, Pages 415–418, https://doi.org/10.1093/analys/ans011 Published: 16 February 2012

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• Strictly Primitive Recursive Realizability, II. Completeness with Respect to Iterated Reflection and a Primitive Recursive $\omega$-Rule

  Notre Dame Journal of Formal Logic · 1998-07-01 · 2 citations

  article1st authorCorresponding

  The notion of strictly primitive recursive realizability is further investigated, and the realizable prenex sentences, which coincide with primitive recursive truths of classical arithmetic, are characterized as precisely those provable in transfinite progressions $\{\mathrm{PRA}(b) \vert b \in \underline{\mathrm{O}}\}$ over a fragment $\mbox{PR-}(\Sigma^{0}_{1}\mbox{-IR})$ of intuitionistic arithmetic. The progressions are based on uniform reflection principles of bounded complexity iterated along initial segments of a primitive recursively formulated system $\mathrm{\underline{O}}$ of notations for constructive ordinals. A semiformal system closed under a primitive recursively restricted $\omega$-rule is described and proved equivalent to the transfinite progressions with respect to the prenex sentences.

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• Elementary realizability

  Journal of Philosophical Logic · 1997-06-01 · 3 citations

  article1st authorCorresponding
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Frequent coauthors

• Arnold Koslow

  City University of New York

  1 shared

• J.T. Cain

  1 shared