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Stability of Weak Second-Order Semantics

László Csirmaz
Studia Logica: An International Journal for Symbolic Logic
Vol. 47, No. 3 (1988), pp. 193-202
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015374
Page Count: 10
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Stability of Weak Second-Order Semantics
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Abstract

By extending the underlying data structure by new elements, we also extend the intput/output relation generated by a program i.e., no existing run is killed, and no new one lying entirely in the old structure is created. We investigate this stability property for the weak second order semantics derived from nonstandard time models. It turns out that the light face, i.e., parameterless collection principle always induces stable semantics, but the bold face one may be unstable. We give an example where an elementary extension kills a 'bold face run', showing also that the light face semantics is strictly weaker than the bold face one.

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