# A Direct Version of Veldman's Proof of Open Induction on Cantor Space via Delimited Control Operators

@inproceedings{Ilik2013ADV, title={A Direct Version of Veldman's Proof of Open Induction on Cantor Space via Delimited Control Operators}, author={Danko Ilik and Keiko Nakata}, booktitle={TYPES}, year={2013} }

First, we reconstruct Wim Veldman's result that Open Induction on Cantor space can be derived from Double-negation Shift and Markov's Principle. In doing this, we notice that one has to use a countable choice axiom in the proof and that Markov's Principle is replaceable by slightly strengthening the Double-negation Shift schema. We show that this strengthened version of Double-negation Shift can nonetheless be derived in a constructive intermediate logic based on delimited control operators… CONTINUE READING

#### Topics from this paper.

4 Citations

An interpretation of the Sigma-2 fragment of classical Analysis in System T

- Mathematics, Computer Science
- 2013

2

Perspectives for proof unwinding by programming languages techniques

- Mathematics, Computer Science
- 2017

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 24 REFERENCES

Brouwer’s Fan Theorem as an axiom and as a contrast to Kleene’s alternative

- Mathematics, Biology
- 2014

25

A Constructive Proof of Dependent Choice, Compatible with Classical Logic

- Mathematics, Computer Science
- 2012

30

Applied Proof Theory - Proof Interpretations and their Use in Mathematics

- Mathematics, Computer Science
- 2008

356