New answers tagged theories-of-arithmetic
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Can this theory interpret Peano arithmetic?
Yes we can interpret Peano Arithmetic, but only by restricting to a subclass. As I noted in a comment, there's a model of your axioms where the assertion $\forall n, \neg(n<n)$ fails, so we cannot ...
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Accepted
Are PA and Counting Theory synonymous\bi-interpretable?
For bi-interpretability, it seems like you’ve mostly answered the question yourself. You’ve described interpretations $\newcommand{\PA}{\mathsf{PA}}\newcommand{\CT}{\mathsf{CT}}\newcommand{\S}{\mathsf{...
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Accepted
To which arithmetic\set theory this theory is bi-interpretable?
Your theory is true in the one-element universe $\{a\}$ in which $a<a$ is true and $a\in a$ is false. The order transitivity holds trivially in this case; the finiteness axiom holds vacuously; and ...
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