Toward the Limits of the Tennenbaum Phenomenon

We consider the theory and its weak fragments in the language of arithmetic expanded with the functional symbol . We prove that and its weak fragments, down to and , are subject to the Tennenbaum phenomenon with respect to , , and . For the last two theories it is still unknown if they may have nonstandard recursive models in the usual language of arithmetic
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DOI 10.1305/ndjfl/1039700698
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