A problem in the theory of constructive order types

Journal of Symbolic Logic 35 (1):119-121 (1970)
  Copy   BIBTEX

Abstract

J. N. Crossley [1] raised the question of whether the implication 2 + A = A ⇒ 1 + A = A is true for constructive order types (C.O.T.'s). Using an earlier definition of constructive order type, A. G. Hamilton [2] presented a counterexample. Hamilton left open the general question, however, since he pointed out that Crossley considers only orderings which can be embedded in a standard dense r.e. ordering by a partial recursive function, and that his counterexample fails to meet this requirement. We resolve the question by finding a C.O.T. A which meets Crossley's requirement and such that 2 + A = A but 1 + A ≠ A. At the suggestion of A. B. Manaster and A. G. Hamilton we easily extend this construction to show that for any n ≧ 2, there is a C.O.T. A such that n + A = A but m + A ≠ A for 0 < m < n. Hence, Theorem 3 of [2] and all of its corollaries hold with the new definition of C.O.T. The construction is not difficult and requires no priority argument. The techniques are similar to those developed in [3], but no outside results are needed here.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,593

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Constructive order types on cuts.Robert I. Soare - 1969 - Journal of Symbolic Logic 34 (2):285-289.
Syntactic calculus with dependent types.Aarne Ranta - 1998 - Journal of Logic, Language and Information 7 (4):413-431.
Constructive order types, II.John N. Crossley - 1966 - Journal of Symbolic Logic 31 (4):525-538.
Constructive order types.John N. Crossley - 1969 - London,: North-Holland Pub. Co..

Analytics

Added to PP
2009-01-28

Downloads
60 (#241,099)

6 months
17 (#107,161)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references