Meta-theory is the term for the theory in which mathematics is formalized (often PA, ZFC or similar theories). Meta-mathematical statements are statements which are evaluated at the level of the meta-theory rather than the theory. This tag is for questions regarding meta-mathematical theories, and ...

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An “internal” condition on $T$ so that for the standard provability predicate, $T$ proves $\text{Pf}(\underline S)$ implies $T$ proves $S$?

This is probably quite basic, but I'd like to make sure I got this right. Regarding the proof of Goedel's first incompleteness theorem, say that we have $T$ containing $PA$ effectively axiomatizable ...
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Maths, esp. Godel, and poetry

At the risk of being an interloper: I'm a poet with a bit of mathematical training. Right now I've got a grant from the Arts Council of Northern Ireland to write a collection (loosely) based on the ...
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Where can I find an ontology of algebraic structures?

A group is a monoid where every element admits an inverse, A ring is a monoid under multiplication that distributes over a commutative group A field is a ring whose non-zero elements form a group ...
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First-Order Logic: Non-Normal Model of Sentences True in all Normal Models?

Let $\mathcal{L}$ be a first-order language with quantifier $\forall$, connectives $\neg$ and $\rightarrow$, a two-place predicate $E$ and a one-place function symbol $f$. There are no other ...