Skolem's paradox and constructivism

@article{McCarty1987SkolemsPA,
  title={Skolem's paradox and constructivism},
  author={Charles McCarty and Neil Tennant},
  journal={Journal of Philosophical Logic},
  year={1987},
  volume={16},
  pages={165-202}
}
  • C. McCarty, N. Tennant
  • Published 1 May 1987
  • Mathematics, Computer Science
  • Journal of Philosophical Logic
Les AA. soutiennent que les mathematiques intuitionnistes ne donnent pas lieu au paradoxe de Skolem. Ils soutiennent de plus que les preuves connues du theoreme de Lowenheim-Skolem sont inacceptables d'un point de vue constructiviste. Ils en tirent les consequences pour une philosophie des mathematiques intuitionniste 
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References

SHOWING 1-10 OF 36 REFERENCES
Syntactic Translations and Provably Recursive Functions
  • D. Leivant
  • Mathematics, Computer Science
    J. Symb. Log.
  • 1985
On montre que les resultats de conservation pour les theories classiques sur les theories intuitionnistes correspondantes peuvent etre obtenus directement et tres facilement a partir de l'observation
Skolem and the Skeptic
structure that all progressions have in common in virtue of being progressions. It is not a science concerned with particular objects-the numbers. The search for which independently identifiable
Constructive Validity is Nonarithmetic
TLDR
It follows constructively from weak versions of Markov's principle and Church's thesis that logical validity for single sentences is not arithmetically definable and is a direct consequence of the constructive modeltheoretic fact that one can prove the categoricity of first-order Heyting arithmetic.
Axiom of choice and complementation
It is shown that an intuitionistic model of set theory with the axiom of choice has to be a classical oneO A topos 6 is a category which has finite limits (i.e. finite products, intersections and a
On Weak Completeness of Intuitionistic Predicate Logic
Suppose the r i -placed relation symbols P i , 1 ≦ i ≦ k , are all the non-logical constants occurring in the closed formula , also written as , of Heyting's predicate calculus (HPC). Then HPC is
Another Intuitionistic Completeness Proof
In March 1973, W. Veldman [1] discovered that, by a slight modification of a Kripke-model, it was possible to give an intuitionistic proof of the completeness-theorem for the intuitionistic predicate
Extending Godel's Negative Interpretation to ZF
  • W. Powell
  • Mathematics, Philosophy
    J. Symb. Log.
  • 1975
TLDR
It is shown that Godel's negative interpretation can be extended to Zermelo-Fraenkel set theory and an inner model S is defined in which the axioms of Zermel- FraenkelSet theory are true.
Advanced Logic for Applications
I. Henkin Sets and the Fundamental Theorem.- II. Derivation Rules and Completeness.- III. Gentzen Systems and Constructive Completeness Proofs.- IV. Quantification Theory with Identity and Functional
An undecidable arithmetical statement
Publisher Summary This chapter provides an alternative proof of the existence of formally undecidable sentences. Instead of the arithmetization of syntax and the diagonal process which were used by
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