On the Well Extension of Partial Well Orderings
Abstract
In this paper, we study the well extension of strict(irreflective) partial well orderings. We first prove that any partially well-ordered structure <A, R> can be extended to a well-ordered one. Then we prove that every linear extension of <A, R> is well-ordered if and only if A has no infinite totally unordered subset under R.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2015
- DOI:
- 10.48550/arXiv.1503.06514
- arXiv:
- arXiv:1503.06514
- Bibcode:
- 2015arXiv150306514L
- Keywords:
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- Computer Science - Logic in Computer Science