Abstract
The H theory of equality E H has the axioms:
-
(a)
x = x.
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(b)
x = y → y = x.
-
(c)
x = y → (y = z → x = z).
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(d)
For any wff A x = y → (A (x) → A (y)).
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Note
The section on end-extension is new. The rest is pretty standard. The results on fragments of arithmetic are based on a paper of K. Gordon and D. deJongh.
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© 1981 Springer Science+Business Media Dordrecht
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Gabbay, D.M. (1981). Theories in HPC 2. In: Semantical Investigations in Heyting’s Intuitionistic Logic. Synthese Library, vol 148. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2977-2_13
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DOI: https://doi.org/10.1007/978-94-017-2977-2_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8362-3
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