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.

Enayat Theories

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



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.

Finite Axiomatizability using additional predicates

This paper supplements the work of Kleene [9] on axiomatizability of theories with identity and notes that, as a consequence of a recent result of Tarski, the new additional predicates required can be reduced to one binary predicate in (1), (2), and (3).

Theories of linear order

LetT be a complete theory of linear order; the language ofT may contain a finite or a countable set of unary predicates. We prove the following results. (i) The number of nonisomorphic countable

The Interpretation Existence Lemma

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

Relative Truth Definability of Axiomatic Truth Theories

  • 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

Metamathematics of First-Order Arithmetic

This chapter discusses Arithmetic as Number Theory, Set Theory and Logic, Fragments and Combinatorics, and Models of Fragments of Arithmetic.

Finite Axiomatizability of Theories in the Predicate Calculus Using Additional Predicate Symbols

Admissible sets and structures

Let's read! We will often find out this sentence everywhere. When still being a kid, mom used to order us to always read, so did the teacher. Some books are fully read in a week and we need the

Descriptive Complexity

  • N. Immerman
  • Computer Science
    Graduate Texts in Computer Science
  • 1999
The core of the book is contained in Chapters 1 through 7, although even here some sections can be omitted according to the taste and interests of the instructor, and the remaining chapters are more independent of each other.