A five element basis for the uncountable linear orders

By Justin Tatch Moore. 2005

75 citations recorded by the source corpus.

In this paper I will show that it is relatively consistent with the usual axioms of mathematics (ZFC) together with a strong form of the axiom of infinity (the existence of a supercompact cardinal) that the class of uncountable linear orders has a five element basis. In fact such a basis follows from the Proper Forcing Axiom, a strong form of the Baire Category Theorem. The elements are X, ¥o1, ¥o.1, C, C. where X is any suborder of the reals of cardinality .1 and C is any Countryman line. This confirms a longstanding conjecture of Shelah.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/18780fdd608ac9756d4dba43ae9119f0a302725a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Ilijas Farah
2. Justin Tatch Moore

In Geometry and Topology

1. Ilijas Farah
2. Justin Tatch Moore
3. Franklin D. Tall
4. Andrés Navas
5. Marion Scheepers

In Mathematical Physics

1. Ilijas Farah
2. Justin Tatch Moore
3. Franklin D. Tall
4. Andrés Navas
5. Marion Scheepers

Citations in the corpus

• ALL AUTOMORPHISMS OF THE CALKIN ALGEBRA ARE INNER (2007, methodology): “The latter is a strengthening of the Baire Category Theorem and besides its applications to the theory of liftings it can be used to find other combinatorial reductions ([39, §8], [30]).”
• A solution to the L space problem (2005, background): “In [ 18 ], I confirmed that Conjecture 4 follows from PFA.”