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- Laurence Kirby
- Math. Log. Q.
- 2007

Ordinal addition and multiplication can be extended in a natural way to all sets. I survey the structure of the sets under these operations. In particular, the natural partial ordering associated with addition of sets is shown to be a tree. This allows us to prove that any set has a unique representation as a sum of additively irreducible sets, and that the… (More)

- Laurence Kirby
- Arch. Math. Log.
- 2008

- Laurence Kirby
- Notre Dame Journal of Formal Logic
- 2009

- Laurence Kirby
- Math. Log. Q.
- 2013

- Laurence Kirby
- Math. Log. Q.
- 2010

- Laurence Kirby
- Math. Log. Q.
- 2015

- Laurence Kirby, L. Kirby
- 2008

This article defines a hierarchy on the hereditarily finite sets which reflects the way sets are built up from the empty set by repeated adjunction, the addition to an already existing set of a single new element drawn from the already existing sets. The structure of the lowest levels of this hierarchy is examined, and some results are obtained about the… (More)

- Laurence Kirby
- Notre Dame Journal of Formal Logic
- 2015

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