Journal of Symbolic Logic

Bounded modified realizability

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

https://projecteuclid.org/euclid.jsl/1140641178

Digital Object Identifier
doi:10.2178/jsl/1140641178

Mathematical Reviews number (MathSciNet)
MR2210071

Zentralblatt MATH identifier
1100.03050

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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