3
$\begingroup$

In Bishop's constructive mathematics, is there any literature on a possible version of the weak König's lemma, or of the compactness theorem for countable models? There is some related information here but not enough to resolve the issue.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
8
$\begingroup$

A detailed analysis of König's lemma in Bishop-style constructivism was carried out by Hajime Ishihara, Josef Berger and Helmut Schwichtenberg. Some references:

  1. Hajime Ishihara, Weak König’s lemma implies Brouwer’s fan theorem: a direct proof, Notre Dame J. Formal Logic 47 (2006), no. 2, 249--252.

  2. H. Schwichtenberg: A direct proof of the equivalence between Brouwer’s fan theorem and König’s lemma with a uniqueness hypothesis. J. UCS 11(12): 2086-2095 (2005)

  3. Josef Berger, Hajime Ishihara, Peter Schuster: The Weak Koenig Lemma, Brouwer's Fan Theorem, De Morgan's Law, and Dependent Choice. Reports on Mathematical Logic 47: 63-86 (2012)

Improve this answer
$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.