Locally countable orderings

More documents

Recommendations

Info

Main Question Question For any locally countable Σ 1 1 partial order P = 〈2ω , ≤ P 〉, does there exist a nonmeasurable antichain in P?
Higher recursion theory I x ≤ h y if x is ∆ 1 1 (z) definable. x ≤ h y is a Π 1 1 -relation. Theorem (Harrison ) For any real z and countable Σ 1 1 (z) set Z ⊂ 2ω , if x ∈ Z , then x ≤ h z. Corollary If P = 〈2 ω , ≤ P 〉 is a Σ 1 1 locally countable partial order, then for any x, y ∈ 2 ω , x ≤ P y implies x ≤ h y.
Page 1 and 2: Locally countable orderings Liang Y
Page 3 and 4: The basic Refs are Downey and Hirsc
Page 5: Motivation Counting the antichains.
Page 9 and 10: Proposition 1 Assume ZFC + V = L, t
Page 11 and 12: Definition Given a string σ ∈ 2
Page 13 and 14: 0-law Proposition If X ⊆ 2 ω and
Page 15 and 16: Calculating the complexity I Propos
Page 17 and 18: Attacking the question I Lemma For
Page 19 and 20: continued. Then µ({z ∈ 2 ω |
Page 21 and 22: continued. Define a ∆ 1 2 (z)-seq
Page 23 and 24: Solving the question Theorem For an
Page 25 and 26: Applications to some specific order
Page 27 and 28: Possible generalizations II We say
Page 29: Thanks

Locally countable orderings

Create successful ePaper yourself

Delete template?

Save as template?