In this paper, we show that the predicate logics of consistent
extensions of Heyting’s Arithmetic plus Church’s Thesis
with uniqueness condition are complete
Π⁰₂. Similarly, we show that the
predicate logic of HA*, i.e. Heyting’s
Arithmetic plus the Completeness Principle (for
HA*) is complete
Π⁰₂. These results extend the known
results due to Valery Plisko. To prove the results we adapt
Plisko’s method to use Tennenbaum’s Theorem to prove
‘categoricity of interpretations’ under certain
assumptions.
Publié le : 2006-12-14
Classification:
Relative interpretations, predicate logics of arithmetical theories, constructive logic,
03B20, 03B25, 03F25, 03F30, 03F45
@article{1164060457,
author = {Visser, Albert},
title = {Predicate logics of constructive arithmetical theories},
journal = {J. Symbolic Logic},
volume = {71},
number = {1},
year = {2006},
pages = { 1311-1326},
language = {en},
url = {http://dml.mathdoc.fr/item/1164060457}
}
Visser, Albert. Predicate logics of constructive arithmetical theories. J. Symbolic Logic, Tome 71 (2006) no. 1, pp. 1311-1326. http://gdmltest.u-ga.fr/item/1164060457/