Journal of Symbolic Logic

Bounded modified realizability

Fernando Ferreira and Ana Nunes

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Abstract

We define a notion of realizability, based on a new assignment of formulas, which does not care for precise witnesses of existential statements, but only for bounds for them. The novel form of realizability supports a very general form of the FAN theorem, refutes Markov’s principle but meshes well with some classical principles, including the lesser limited principle of omniscience and weak König’s lemma. We discuss some applications, as well as some previous results in the literature.

Article information

Source
J. Symbolic Logic, Volume 71, Issue 1 (2006), 329-346.

Dates
First available in Project Euclid: 22 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1140641178

Digital Object Identifier
doi:10.2178/jsl/1140641178

Mathematical Reviews number (MathSciNet)
MR2210071

Zentralblatt MATH identifier
1100.03050

Subjects
Primary: 03F35: Second- and higher-order arithmetic and fragments [See also 03B30] 03F50: Metamathematics of constructive systems 03F10: Functionals in proof theory
Secondary: 03F25: Relative consistency and interpretations

Keywords
Realizability bounds semi-intuitionism conservativeness

Citation

Ferreira, Fernando; Nunes, Ana. Bounded modified realizability. J. Symbolic Logic 71 (2006), no. 1, 329--346. doi:10.2178/jsl/1140641178. https://projecteuclid.org/euclid.jsl/1140641178


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