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How to glue analysis models

Published online by Cambridge University Press:  12 March 2014

D. Van Dalen
D. Van Dalen*
Affiliation:
Mathematisch Instituut, Rijksuniversiteit Utrecht, Utrecht, The Netherlands
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Extract

Among the more traditional semantics for intuitionistic logic the Beth and the Kripke semantics seem well-suited for direct manipulations required for the derivation of metamathematical results. In particular Smoryński demonstrated the usefulness of Kripke models for the purpose of obtaining closure properties for first-order arithmetic, [S], and second-order arithmetic, [J-S]. Weinstein used similar techniques to handle intuitionistic analysis, [W]. Since, however, Beth-models seem to lend themselves better for dealing with analysis, cf. [D], we have developed a somewhat more liberal semantics, that shares the features of both Kripke and Beth semantics, in order to obtain analogues of Smoryński's collecting operations, which we will call Smoryński-glueing, in line with the categorical tradition.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 49 , Issue 4 , December 1984 , pp. 1339 - 1349
Copyright
Copyright © Association for Symbolic Logic 1984

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References

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