On Guaspari's problem about partially conservative sentences

نویسندگان

چکیده

We investigate sentences which are simultaneously partially conservative over several theories. First, we generalize Bennet's results on this topic to the case of more than two In particular, for any finite family {Ti}i≤k consistent r.e. extensions Peano Arithmetic, give a necessary and sufficient condition existence Πn sentence is unprovable in Ti Σn-conservative all i≤k. Secondly, prove that such theories, there exists Σn Πn-conservative each these This constitutes positive solution particular Guaspari's problem. Finally, demonstrate non-implications among related properties families

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ژورنال

عنوان ژورنال: Annals of Pure and Applied Logic

سال: 2022

ISSN: ['0168-0072', '1873-2461']

DOI: https://doi.org/10.1016/j.apal.2022.103087