# Tagged Questions

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### Axiom to exclude nonstandard natural numbers

In Peano Arithmetic, the induction axiom states that there is no proper subset of the natural numbers that contains 0 and is closed under the successor function. This is intended to rule out the ...

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### Set Theory inside Arithmetics via the Ackermann Yoga

Among the basic results of logic which, simple as they are, never fail to intrigue me, is Ackermann's interpretation of $ZF$-Infinity in $PA$ (see for refs this MO question and here for an excellent ...

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### Is Robinson Arithmetic biinterpretable with some theory in LST?

Let ZFC$^{\text{fin}}$ be ZFC minus the axiom of infinity plus the negation of the axiom of infinity. It is well-known that ZFC$^{\text{fin}}$ is biinterpretable with Peano Arithmetic. In this sense ...

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### Incompleteness and nonstandard models of arithmetic

The following are a collection of doubts, some of which shall have concrete answers while others may have not. Any kind of help will be welcome.
Reading Peter Smith's "GĂ¶del Without (Too Many) ...

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**3**answers

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### “Interesting” properties of sets of natural numbers

On Wikipedia, there is a list of properties of sets of reals, which are in some sense "interesting": just have a look.
I could not find a comparable list of properties of sets of natural numbers ...