Computability-theoretic and proof-theoretic aspects of partial and linear orderings

DOI10.1007/BF02783429zbMath1044.03043OpenAlexW2028592975MaRDI QIDQ1425651

Rodney G. Downey, Steffen Lempp, Denis R. Hirschfeldt, D. Reed Solomon

Publication date: 17 March 2004

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02783429

zbMATH Keywords

combinatoricsproof theoryreverse mathematicspartial orderinglinear orderingSzpilrajn's theoremeffective content

Mathematics Subject Classification ID

Partial orders, general (06A06) Combinatorics of partially ordered sets (06A07) Foundations of classical theories (including reverse mathematics) (03B30) Total orders (06A05) Second- and higher-order arithmetic and fragments (03F35) Theory of numerations, effectively presented structures (03D45)

Related Items (10)

Equivalence between Fraïssé's conjecture and Jullien's theorem ⋮ Open Questions in Reverse Mathematics ⋮ There are 2^{ℵ₀} many 𝐻-degrees in the random reals ⋮ Countably complementable linear orderings ⋮ A constructive picture of Noetherian conditions and well quasi-orders ⋮ Some Questions in Computable Mathematics ⋮ Up to equimorphism, hyperarithmetic is recursive ⋮ On the Equimorphism Types of Linear Orderings ⋮ Maximal compatible extensions of partial orders ⋮ Linear extensions of partial orders and reverse mathematics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Countable algebra and set existence axioms
• Extending partial orders to dense linear orders
• Effective procedures in field theory
• Effective content of field theory
• Ordered Groups: A Case Study in Reverse Mathematics
• Computable Algebra, General Theory and Theory of Computable Fields
• ∏ 0 1 Classes and Degrees of Theories
• Ramsey's theorem and recursion theory

This page was built for publication: Computability-theoretic and proof-theoretic aspects of partial and linear orderings