Laver's theorem, in order theory, states that order embeddability of countable total orders is a well-quasi-ordering. That is, for every infinite sequence of totally-ordered countable sets, there exists an order embedding from an earlier member of the sequence to a later member. This result was previously known as Fraïssé's conjecture, after Roland Fraïssé, who conjectured it in 1948;[1] Richard Laver proved the conjecture in 1971. More generally, Laver proved the same result for order embeddings of countable unions of scattered orders.[2][3]
Inreverse mathematics, the version of the theorem for countable orders is denoted FRA (for Fraïssé) and the version for countable unions of scattered orders is denoted LAV (for Laver).[4] In terms of the "big five" systems of second-order arithmetic, FRA is known to fall in strength somewhere between the strongest two systems, 
-comprehension", Journal of Mathematical Logic, 17 (2): 1750006, 12, doi:10.1142/S0219061317500064, MR 3730562
|
| |
|---|---|
| |
| Key concepts |
|
| Results |
|
| Properties & Types (list) |
|
| Constructions |
|
| Topology & Orders |
|
| Related |
|
