Introduces two first-order theories of trees, revealing mutual interpretations with other theories.
We introduce two weak first-order theories of weighted and labelled finite trees, T*† and T*‡, respectively. It is proved that T*† and T*‡ are mutually interpretable with other previously studied elementary theories of ‘undecorated’ finite trees, as well as with Robinson Arithmetic, Q, and a host of other weak first-order theories of numbers, strings, sets and sequences.
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Zlatan Damnjanovic (2025) studied this question.
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