Book contents
- Frontmatter
- Contents
- Preface
- Participants Photograph
- Generic absoluteness for Σ1 formulas and the continuum problem
- Axioms of generic absoluteness
- Generalised dynamic ordinals — universal measures for implicit computational complexity
- The Worm principle
- “One is a lonely number”: logic and communication
- Computable versions of the uniform boundedness theorem
- Symmetry of the universal computable function: A study of its automorphisms, homomorphisms and isomorphic embeddings
- PCF theory and Woodin cardinals
- Embedding finite lattices into the computably enumerable degrees — a status survey
- Dimension theory inside a homogeneous model
- Reals which compute little
- Bisimulation invariance and finite models
- Choice principles in constructive and classical set theories
- Ash's theorem for abstract structures
- Martin-Löf random and PA-complete sets
- Learning and computing in the limit
- References
Embedding finite lattices into the computably enumerable degrees — a status survey
Published online by Cambridge University Press: 31 March 2017
Book contents
- Frontmatter
- Contents
- Preface
- Participants Photograph
- Generic absoluteness for Σ1 formulas and the continuum problem
- Axioms of generic absoluteness
- Generalised dynamic ordinals — universal measures for implicit computational complexity
- The Worm principle
- “One is a lonely number”: logic and communication
- Computable versions of the uniform boundedness theorem
- Symmetry of the universal computable function: A study of its automorphisms, homomorphisms and isomorphic embeddings
- PCF theory and Woodin cardinals
- Embedding finite lattices into the computably enumerable degrees — a status survey
- Dimension theory inside a homogeneous model
- Reals which compute little
- Bisimulation invariance and finite models
- Choice principles in constructive and classical set theories
- Ash's theorem for abstract structures
- Martin-Löf random and PA-complete sets
- Learning and computing in the limit
- References
- Type
- Chapter
- Information
- Logic Colloquium '02 , pp. 206 - 229Publisher: Cambridge University PressPrint publication year: 2006
References
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[2] and , Lattice embeddings into the recursively enumerable degrees The Journal of Symbolic Logic, vol. 51 (1986), no. 2, pp. 257–272.
[3] and , Lattice embeddings into the recursively enumerable degrees. II The Journal of Symbolic Logic, vol. 54 (1989), no. 3, pp. 735–760.
[4] , Lattice nonembeddings and initial segments of the recursively enumerable degrees Annals of Pure and Applied Logic, vol. 49 (1990), no. 2, pp. 97–119.
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[6] , Lower bounds for pairs of recursively enumerable degrees Proceedings of the London Mathematical Society. Third Series, vol. 16 (1966), pp. 537–569.
[7] , Embedding nondistributive lattices in the recursively enumerable degrees Conference in Mathematical Logic—London '70 (Proc. Conf., Bedford Coll., London, 1970), Lecture Notes in Math., vol. 255, Springer, Berlin, 1972, pp. 149–177.
[8] and , Not every finite lattice is embeddable in the recursively enumerable degrees Advances in Mathematics, vol. 37 (1980), no. 1, pp. 74–82.
[9] and , A finite lattice without critical triple that cannot be embedded into the enumerable Turing degrees Annals of Pure and Applied Logic, vol. 87 (1997), no. 2, pp. 167–185.
[10] , Admissible ordinals and priority arguments Cambridge Summer School in Mathematical Logic (Cambridge, 1971), Springer, Berlin, 1973, pp. 311–344.
[11] , A necessary and sufficient condition for embedding ranked finite partial lattices into the computably enumerable degrees Annals of Pure and Applied Logic, vol. 94 (1998), no. 1-3, pp. 143–180.
[12] , A necessary and sufficient condition for embedding principally decomposable finite lattices into the computably enumerable degrees Annals of Pure and Applied Logic, vol. 101 (2000), no. 2-3, pp. 275–297.
[13] , Embeddings into the computably enumerable degrees Computability Theory and its Applications (Boulder, CO, 1999), Amer. Math. Soc., Providence, RI, 2000, pp. 191–205.
[14] and , Extension of embeddings in the computably enumerable degrees Annals of Mathematics. Second Series, vol. 154 (2001), no. 1, pp. 1–43.
[15] , Recursively Enumerable Sets and Degrees, Perspectives inMathematical Logic, Springer, Berlin, 1987.
[16] , Sublattices of the recursively enumerable degrees Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, vol. 17 (1971), pp. 273–280.
[17] , A minimal pair of recursively enumerable degrees The Journal of Symbolic Logic, vol. 31 (1966), pp. 159–168
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