author={Fedor Pakhomov and Albert Visser},
  journal={The Journal of Symbolic Logic},
  pages={343 - 358}
  • F. PakhomovA. Visser
  • Published 5 December 2017
  • Computer Science, Mathematics
  • The Journal of Symbolic Logic
Abstract In this paper, we study finitely axiomatizable conservative extensions of a theory U in the case where U is recursively enumerable and not finitely axiomatizable. Stanisław Krajewski posed the question whether there are minimal conservative extensions of this sort. We answer this question negatively. Consider a finite expansion of the signature of U that contains at least one predicate symbol of arity ≥ 2. We show that, for any finite extension α of U in the expanded language that is… 

The small‐is‐very‐small principle

  • A. Visser
  • Mathematics, Computer Science
    Math. Log. Q.
  • 2019
The central result of this paper is the small‐is‐very‐small principle for restricted sequential theories, which says roughly that whenever the given theory shows that a definable property has a small witness, then it shows that theProperty has a very small witness: i.e., a witness below a given standard number.

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In this paper we study solution attempts for a problem posed by Ali Enayat: can there be a finitely axiomatized consistent sequential theory that interprets itself plus the (sentential or



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The present paper contains a fairly detailed verification of a reasonably general form of the Interpretation Existence Lemma. In first approximation, this lemma tells us that if a theory U proves the

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  • K. Fujimoto
  • Philosophy
    The Bulletin of Symbolic Logic
  • 2010
Abstract The present paper suggests relative truth definability as a tool for comparing conceptual aspects of axiomatic theories of truth and gives an overviewof recent developments of axiomatic

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On Q

  • A. Visser
  • Philosophy, Mathematics
    Soft Comput.
  • 2017
This paper proves a basic result that says that, in a sense explained in the paper, Q can be split into two parts, and proves some consequences of this result.